comment {

  These formulas involve lots of interesting math.
  
  All formulas (except FastJulia) written by Tim Coe.
  Last updated September 21, 2002.
}


Manseig {
init:
  complex angl = (sqrt(@start*@start+4)-@start)/2
  angl = 1/(@cfrac2 + angl)
  angl = 1/(@cfrac1 + angl)
  angl = exp(angl*#pi*(0,2))/2
  angl = angl - sqr(angl)
  z = #pixel
loop:
  z = sqr(z) + angl
bailout:
  |z| <= @bailout
default:
  title = "Mandel to Seigel"
  center = (-0.5, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac1
    caption = "Cont Frac 1"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac2
    caption = "Cont Frac 2"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 4.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "FastJulia"
  seed = start
  bailout = bailout
}


FastJulia(ORIGIN) {
builtin:
  type = 2
default:
  title = "Built-in fast Julia"
  param seed
    caption = "Julia seed"
    default = (-1.25, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param bailout
    caption = "Bailout value"
    default = 4.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "FastMandel"
  bailout = bailout
}


Manphuge {
; Generic Mandelbrot set
init:
  float endval = exp(40)
  if (@bailout < 80)
    endval = exp(0.5*@bailout)
  endif
  z = @start
loop:
  if real(z) < 40 && real(z) < 0.5*@bailout
    z = exp(z) + #pixel
  elseif real(z) - @bailout < -40
    if ((imag(z)/(2*#pi)) - floor(imag(z)/(2*#pi))) < 0.25
      z = endval
    elseif ((imag(z)/(2*#pi)) - floor(imag(z)/(2*#pi))) > 0.75
      z = endval
    else
      z = (-45,0)
    endif
  elseif |exp(z - @bailout) + 1| < 1
    z = (-45,0)
  else
    z = endval
  endif
bailout:
  real(z) - 1 <= @bailout
default:
  title = "Manphuge"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (-45,0)
    hint = "Perturbation. Use (0,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (2,0)
    hint = "This defines the power of the Mandelbrot set. Use (2,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Julphuge"
  seed = #pixel
  power = power
  bailout = bailout
}


Julphuge {
; Generic Julia set
init:
  float endval = exp(40)
  if (@bailout < 80)
    endval = exp(0.5*@bailout)
  endif
  z = #pixel
loop:
  if real(z) < 40 && real(z) < 0.5*@bailout
    z = exp(z) + @seed
  elseif real(z) - @bailout < -40
    if ((imag(z)/(2*#pi)) - floor(imag(z)/(2*#pi))) < 0.25
      z = endval
    elseif ((imag(z)/(2*#pi)) - floor(imag(z)/(2*#pi))) > 0.75
      z = endval
    else
      z = (-45,0)
    endif
  elseif |exp(z - @bailout) + 1| < 1
    z = (-45,0)
  else
    z = endval
  endif
bailout:
  real(z) - 1 <= @bailout
default:
  title = "Julphuge"
  param seed
    caption = "Julia seed"
    default = (-1, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (2,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Manphuge"
  power = power
  bailout = bailout
}

Manolog {
; Generic Mandelbrot set
init:
  z = @start
loop:
  z = z + (z + 1)*sqr(z) + #pixel
bailout:
  |z| <= @bailout
default:
  title = "Manolog"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (-0.333333333333333333333,0.4714045207910316829)
    hint = "Perturbation. Use (0,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (2,0)
    hint = "This defines the power of the Mandelbrot set. Use (2,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Junolog"
  seed = #pixel
  power = power
  bailout = bailout
}


Junolog {
; Generic Julia set
init:
  z = #pixel
loop:
  z = z + (z + 1)*sqr(z) + @seed
bailout:
  |z| <= @bailout
default:
  title = "Junolog"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (2,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Manolog"
  power = power
  bailout = bailout
}

Dualies {
; Generic Mandelbrot set
init:
  z = @start*sqrt(@power/3)
loop:
  z = z*(sqr(z) + @power) + #pixel
bailout:
  |z| <= @bailout
default:
  title = "Dualies"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (0,1)
    hint = "Perturbation. Use (0,1) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jualies"
  seed = #pixel
  power = power
  bailout = bailout
}


Jualies {
; Generic Julia set
init:
  z = #pixel
loop:
  z = z*(sqr(z) + @power) + @seed
bailout:
  |z| <= @bailout
default:
  title = "Jualies"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Dualies"
  power = power
  bailout = bailout
}

Follow {
; Generic Mandelbrot set
init:
  complex a = -3*#pixel*#pixel
  complex b = -#pixel*(2*#pixel*#pixel - 1)
  z = @start*#pixel
loop:
  z = z*(sqr(z) + a) + b
bailout:
  |z| <= @bailout
default:
  title = "Follow"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jollow"
  seed = #pixel
  power = power
  bailout = bailout
}


Jollow {
; Generic Julia set
init:
  complex a = -3*@seed*@seed
  complex b = -@seed*(2*@seed*@seed - 1)
  z = #pixel
loop:
  z = z*(sqr(z) + a) + b
bailout:
  |z| <= @bailout
default:
  title = "Jollow"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Follow"
  power = power
  bailout = bailout
}

Tritrail {
; Generic Mandelbrot set
init:
  complex pix3 = #pixel*#pixel*#pixel
  complex q = #pixel*(12 - pix3)/(12 - 2*pix3)
  complex a3 = -0.3333333333333333333*(#pixel + q)
  complex a2 = 0.5*#pixel*q
  z = q
loop:
  z = ((0.25*z + a3)*z + a2)*sqr(z) + #pixel
bailout:
  |z| <= @bailout
default:
  title = "Tritrail"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0

    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jritrail"
  seed = #pixel
  power = power
  bailout = bailout
}


Jritrail {
; Generic Julia set
init:
  complex pix3 = @seed*@seed*@seed
  complex q = @seed*(12 - pix3)/(12 - 2*pix3)
  complex a3 = -0.3333333333333333333*(@seed + q)
  complex a2 = 0.5*@seed*q
  z = #pixel
loop:
  z = ((0.25*z + a3)*z + a2)*sqr(z) + @seed
bailout:
  |z| <= @bailout
default:
  title = "Jritrail"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Tritrail"
  power = power
  bailout = bailout
}

Trailfix {
; Generic Mandelbrot set
init:
  complex s = (#pixel*#pixel - 2)^(1/3)
  complex p = sqrt(2)*s/#pixel
  complex r = p - s
  complex q = r*(r - 2*p)/(2*r - 6*p)
  complex a3 = -0.3333333333333333333*(p + q + r)
  complex a2 = 0.5*(p*q + p*r + q*r)
  complex a1 = -p*q*r
  z = q
loop:
  z = (((0.25*z + a3)*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Trailfix"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrailfix"
  seed = #pixel
  power = power
  bailout = bailout
}


Jrailfix {
; Generic Julia set
init:
  complex s = (@seed*@seed - 2)^(1/3)
  complex p = sqrt(2)*s/@seed
  complex r = p - s
  complex q = r*(r - 2*p)/(2*r - 6*p)
  complex a3 = -0.3333333333333333333*(p + q + r)
  complex a2 = 0.5*(p*q + p*r + q*r)
  complex a1 = -p*q*r
  z = #pixel
loop:
  z = (((0.25*z + a3)*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Jrailfix"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trailfix"
  power = power
  bailout = bailout
}

Trail112 {
; Generic Mandelbrot set
init:
  complex p = (#pixel + 1/(120*#pixel) - 1/6)^(-0.25)
  complex q = p*(1 - 6*#pixel)
  complex a4 = -0.25*(2*q + p)
  complex a3 = 0.3333333333333333333*q*(2*p + q)
  complex a2 = -0.5*p*q*q
  z = q
loop:
  z = (((0.2*z + a4)*z + a3)*z + a2)*sqr(z) + p
bailout:
  |z| <= @bailout
default:
  title = "Trail112"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrail112"
  seed = #pixel
  power = power
  bailout = bailout
}


Jrail112 {
; Generic Julia set
init:
  complex p = (@seed + 1/(120*@seed) - 1/6)^(-0.25)
  complex q = p*(1 - 6*@seed)
  complex a4 = -0.25*(2*q + p)
  complex a3 = 0.3333333333333333333*q*(2*p + q)
  complex a2 = -0.5*p*q*q
  z = #pixel
loop:
  z = (((0.2*z + a4)*z + a3)*z + a2)*sqr(z) + p
bailout:
  |z| <= @bailout
default:
  title = "Jrail112"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trail112"
  power = power
  bailout = bailout
}

Trail10n {
; Generic Mandelbrot set
init:
  complex u = 1/#pixel
  complex un1 = u^(@n + 1)
  complex pn1 = u*(@n + 1)*(@n + 2)/((@n + 2)*un1 - (@n + 1)*u*un1 - 1)
  complex p = pn1^(1/(@n + 1))
  complex an2 = 1/(@n + 2)
  complex an1 = -p/(@n + 1)
  complex a0 = u*p - an2*p*pn1 - an1*pn1
  z = a0
loop:
  z = (an2*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Trail10n"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point.  The \
            first critical point has order 1 and the second 0."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrail10n"
  seed = #pixel
  n = n
  bailout = bailout
}


Jrail10n {
; Generic Julia set
init:
  complex u = 1/@seed
  complex un1 = u^(@n + 1)
  complex pn1 = u*(@n + 1)*(@n + 2)/((@n + 2)*un1 - (@n + 1)*u*un1 - 1)
  complex p = pn1^(1/(@n + 1))
  complex an2 = 1/(@n + 2)
  complex an1 = -p/(@n + 1)
  complex a0 = u*p - an2*p*pn1 - an1*pn1
  z = #pixel
loop:
  z = (an2*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jrail10n"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trail10n"
  n = n
  bailout = bailout
}

Trail10n1 {
; Generic Mandelbrot set
init:
  complex u = #pixel
  complex bt = 1
  if @unwrap == 1
    bt = u
    u = sqr(u) + @bp1
  elseif @unwrap == 2
    bt = sqr(u) - 1
    u = 0.25*u*(sqr(u) - 3)*(@bp1 - @bp2) + 0.5*(@bp1 + @bp2)
  endif
  complex un2 = u^(@n + 2)
  complex an3 = 1/(@n + 3)
  complex an2 = -1/(@n + 2)
  complex an1 = 1/(@n + 1)
  complex a = un2*u*(an3 + an2)
  complex b = un2*(an2 + an1)
  complex c = an3 + u*an2
  complex d = an2 + u*an1
  complex qa = b - d
  complex qb = a - c + d
  complex qc = c
  complex qrad = (sqr(qb) - 4*qa*qc)/(sqr(@branchcut*bt)*(u^(2*@inout)))
  complex s = (sqrt(qrad)*@branchcut*bt*(u^@inout) - qb)/(2*qa)
  complex pn2 = -s/(c + d*s)
  complex p = pn2^(1/(@n + 2))
  an2 = (u + s)*p*an2
  an1 = u*s*sqr(p)*an1
  complex a0 = s*p
  z = a0
  if @showbranch && (real(qrad) < -10*abs(imag(qrad)))
    z = 1e15
  endif
loop:
  z = ((an3*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Trail10n1"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point.  The \
            first critical point has order 1 and the second 0."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param bp1
    caption = "Branch Point 1"
    default = (1,0)
    hint = "First branch point to unwrap."
  endparam
  param bp2
    caption = "Branch Point 2"
    default = (1,0)
    hint = "Second branch point to unwrap."
  endparam
  param unwrap
    caption = "Unwrap"
    default = 0
    hint = "This specifies the number of branch points to unwrap.  \
            Currently 0 to 2 are supported."
  endparam
  param showbranch
    caption = "Show branches"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps two and duplicates the rest."
  endparam
  param inout
    caption = "Branch In"
    default = 0
    hint = "This sends branch cuts either in or out.  0 or 3+Order are \
            good values"
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrail10n1"
  seed = #pixel
  n = n
  branchcut = branchcut
  inout = inout
  bailout = bailout
}


Jrail10n1 {
; Generic Julia set
init:
  complex u = @seed
  complex un2 = u^(@n + 2)
  complex an3 = 1/(@n + 3)
  complex an2 = -1/(@n + 2)
  complex an1 = 1/(@n + 1)
  complex a = un2*u*(an3 + an2)
  complex b = un2*(an2 + an1)
  complex c = an3 + u*an2
  complex d = an2 + u*an1
  complex qa = b - d
  complex qb = a - c + d
  complex qc = c
  complex qrad = (sqr(qb) - 4*qa*qc)/(sqr(@branchcut)*(u^(2*@inout)))
  complex s = (sqrt(qrad)*@branchcut*(u^@inout) - qb)/(2*qa)
  complex pn2 = -s/(c + d*s)
  complex p = pn2^(1/(@n + 2))
  an2 = (u + s)*p*an2
  an1 = u*s*sqr(p)*an1
  complex a0 = s*p
  z = 2*#pixel
loop:
  z = ((an3*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jrail10n1"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point."
  endparam
  param inout
    caption = "Branch In"
    default = 0
    hint = "This sends branch cuts either in or out.  0 or 3+Order are \
            good values"
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trail10n1"
  n = n
  bailout = bailout
}

Trail11n1 {
; Generic Mandelbrot set
init:
  complex u = #pixel
  complex un2 = u^(@n + 2)
  complex an4 = 1/(@n + 4)
  complex an3 = -1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = -1/(@n + 1)
  complex a = un2*u*(u*an4 + (1 + u)*an3 + an2)
  complex b = un2*(u*an3 + (1 + u)*an2 + an1)
  complex c = an4 + (1 + u)*an3 + u*an2
  complex d = an3 + (1 + u)*an2 + u*an1
  complex qa = b - d
  complex qb = a - c + d
  complex qc = c
  complex qrad = (sqr(qb) - 4*qa*qc)/(sqr(@branchcut)*(u^(2*@inout)))
  complex s = (sqrt(qrad)*@branchcut*(u^@inout) - qb)/(2*qa)
  complex pn3 = -s/(c + d*s)
  complex p = pn3^(1/(@n + 3))
  an3 = (u + s + 1)*p*an3
  an2 = (u + s + u*s)*sqr(p)*an2
  an1 = u*s*sqr(p)*p*an1
  complex a0 = s*p
  z = a0
  if @showbranch && (real(qrad) < -10*abs(imag(qrad)))
    z = 1e15
  endif
loop:
  z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Trail11n1"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point.  The \
            first critical point has order 1 and the second 0."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param showbranch
    caption = "Show branches"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps two and duplicates the rest."
  endparam
  param inout
    caption = "Branch In"
    default = 0
    hint = "This sends branch cuts either in or out.  0 or 3+Order are \
            good values"
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrail11n1"
  seed = #pixel
  n = n
  branchcut = branchcut
  inout = inout
  bailout = bailout
}


Jrail11n1 {
; Generic Julia set
init:
  complex u = @seed
  complex un2 = u^(@n + 2)
  complex an4 = 1/(@n + 4)
  complex an3 = -1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = -1/(@n + 1)
  complex a = un2*u*(u*an4 + (1 + u)*an3 + an2)
  complex b = un2*(u*an3 + (1 + u)*an2 + an1)
  complex c = an4 + (1 + u)*an3 + u*an2
  complex d = an3 + (1 + u)*an2 + u*an1
  complex qa = b - d
  complex qb = a - c + d
  complex qc = c
  complex qrad = (sqr(qb) - 4*qa*qc)/(sqr(@branchcut)*(u^(2*@inout)))
  complex s = (sqrt(qrad)*@branchcut*(u^@inout) - qb)/(2*qa)
  complex pn3 = -s/(c + d*s)
  complex p = pn3^(1/(@n + 3))
  an3 = (u + s + 1)*p*an3
  an2 = (u + s + u*s)*sqr(p)*an2
  an1 = u*s*sqr(p)*p*an1
  complex a0 = s*p
  z = 2*#pixel
loop:
  z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jrail11n1"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point."
  endparam
  param inout
    caption = "Branch In"
    default = 0
    hint = "This sends branch cuts either in or out.  0 or 3+Order are \
            good values"
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trail11n1"
  n = n
  bailout = bailout
}

Trail20n1 {
; Generic Mandelbrot set
init:
  complex u = #pixel
  complex un2 = u^(@n + 2)
  complex an4 = 1/(@n + 4)
  complex an3 = -1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = -1/(@n + 1)
  complex a = un2*u*(u*an4 + (u + u)*an3 + u*an2)
  complex b = un2*(u*an3 + (u + u)*an2 + u*an1)
  complex c = an4 + (u + u)*an3 + u*u*an2
  complex d = an3 + (u + u)*an2 + u*u*an1
  complex qa = b - d
  complex qb = a - c + d
  complex qc = c
  complex qrad = (sqr(qb) - 4*qa*qc)/(sqr(@branchcut)*(u^(2*@inout)))
  complex s = (sqrt(qrad)*@branchcut*(u^@inout) - qb)/(2*qa)
  complex pn3 = -s/(c + d*s)
  complex p = pn3^(1/(@n + 3))
  an3 = (u + s + u)*p*an3
  an2 = (u*u + s*u + u*s)*sqr(p)*an2
  an1 = u*u*s*sqr(p)*p*an1
  complex a0 = s*p
  z = a0
  if @showbranch && (real(qrad) < -10*abs(imag(qrad)))
    z = 1e15
  endif
loop:
  z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Trail20n1"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point.  The \
            first critical point has order 1 and the second 0."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param showbranch
    caption = "Show branches"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps two and duplicates the rest."
  endparam
  param inout
    caption = "Branch In"
    default = 0
    hint = "This sends branch cuts either in or out.  0 or 3+Order are \
            good values"
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrail20n1"
  seed = #pixel
  n = n
  branchcut = branchcut
  inout = inout
  bailout = bailout
}


Jrail20n1 {
; Generic Julia set
init:
  complex u = @seed
  complex un2 = u^(@n + 2)
  complex an4 = 1/(@n + 4)
  complex an3 = -1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = -1/(@n + 1)
  complex a = un2*u*(u*an4 + (u + u)*an3 + u*an2)
  complex b = un2*(u*an3 + (u + u)*an2 + u*an1)
  complex c = an4 + (u + u)*an3 + u*u*an2
  complex d = an3 + (u + u)*an2 + u*u*an1
  complex qa = b - d
  complex qb = a - c + d
  complex qc = c
  complex qrad = (sqr(qb) - 4*qa*qc)/(sqr(@branchcut)*(u^(2*@inout)))
  complex s = (sqrt(qrad)*@branchcut*(u^@inout) - qb)/(2*qa)
  complex pn3 = -s/(c + d*s)
  complex p = pn3^(1/(@n + 3))
  an3 = (u + s + u)*p*an3
  an2 = (u*u + s*u + u*s)*sqr(p)*an2
  an1 = u*u*s*sqr(p)*p*an1
  complex a0 = s*p
  z = 2*#pixel
loop:
  z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jrail20n1"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point."
  endparam
  param inout
    caption = "Branch In"
    default = 0
    hint = "This sends branch cuts either in or out.  0 or 3+Order are \
            good values"
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trail20n1"
  n = n
  bailout = bailout
}

Trail10n2 {
; Generic Mandelbrot set
init:
  complex u = #pixel
  complex un2 = u^(@n + 2)
  complex an4 = 1/(@n + 4)
  complex an3 = -1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = -1/(@n + 1)
  complex a = un2*u*u*(an4 + an3)
  complex b = 2*un2*u*(an3 + an2)
  complex c = un2*(an2 + an1)
  complex d = an4 + u*an3
  complex g = 2*(an3 + u*an2)
  complex h = an2 + u*an1
  complex s = 0
  complex cr1 = 0.5*(flip(sqrt(3)) - 1)
  complex cr2 = sqr(cr1)
  complex ica3 = 1/(c - h)
  complex ca2 = (b - g + h)*ica3
  complex ca1 = (a - d + g)*ica3
  complex ca0 = d*ica3
  complex cq = (3*ca1 - ca2*ca2)/9
  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
  if real(cr) < 0
    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  endif
  complex wi = cq/w
  complex s0 = w - wi
  complex s1 = w*cr1 - wi*cr2
  complex s2 = w*cr2 - wi*cr1
  if |s0| > |s1|
    s = s0
    s0 = s1
    s1 = s
  endif
  if |s0| > |s2|
    s = s0
    s0 = s2
    s2 = s
  endif
  if |s1| > |s2|
    s = s1
    s1 = s2
    s2 = s
  endif
  s = s1
  if @sheet == 0
    s = s0
  elseif @sheet == 1
    s = s1
  elseif @sheet == 2
    s = s2
  elseif @sheet == 4
    if imag(u) > 0
      s = s0
    endif
  else
    if imag(u) > 0
      s = s2
    endif
  endif
  complex s = s - ca2/3
  complex pn3 = -s/(d + g*s + h*s*s)
  complex p = pn3^(1/(@n + 3))
  an3 = (u + s + s)*p*an3
  an2 = (s*s + s*u + u*s)*sqr(p)*an2
  an1 = u*s*s*sqr(p)*p*an1
  complex a0 = s*p
  z = a0
  if @showbranch
    z = 1e15
  endif
loop:
  z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Trail10n2"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point.  The \
            first critical point has order 1 and the second 0."
  endparam
  param sheet
    caption = "Sheets"
    default = 3
    hint = "This has three sheets.  Choose bottom, middle, top, half \
            bottom half mid, or half mid half top."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param showbranch
    caption = "Show branches"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps two and duplicates the rest."
  endparam
  param inout
    caption = "Branch In"
    default = 0
    hint = "This sends branch cuts either in or out.  0 or 3+Order are \
            good values"
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrail10n2"
  seed = #pixel
  n = n
  branchcut = branchcut
  inout = inout
  bailout = bailout
}


Jrail10n2 {
; Generic Julia set
init:
  complex u = @seed
  complex un2 = u^(@n + 2)
  complex an4 = 1/(@n + 4)
  complex an3 = -1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = -1/(@n + 1)
  complex a = un2*u*(u*an4 + (u + u)*an3 + u*an2)
  complex b = un2*(u*an3 + (u + u)*an2 + u*an1)
  complex c = an4 + (u + u)*an3 + u*u*an2
  complex d = an3 + (u + u)*an2 + u*u*an1
  complex qa = b - d
  complex qb = a - c + d
  complex qc = c
  complex qrad = (sqr(qb) - 4*qa*qc)/(sqr(@branchcut)*(u^(2*@inout)))
  complex s = (sqrt(qrad)*@branchcut*(u^@inout) - qb)/(2*qa)
  complex pn3 = -s/(c + d*s)
  complex p = pn3^(1/(@n + 3))
  an3 = (u + s + u)*p*an3
  an2 = (u*u + s*u + u*s)*sqr(p)*an2
  an1 = u*u*s*sqr(p)*p*an1
  complex a0 = s*p
  z = 2*#pixel
loop:
  z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jrail10n2"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the third critical point."
  endparam
  param inout
    caption = "Branch In"
    default = 0
    hint = "This sends branch cuts either in or out.  0 or 3+Order are \
            good values"
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trail10n2"
  n = n
  bailout = bailout
}

Trail1111 {
; Generic Mandelbrot set
init:
  complex u = 1/#pixel
  complex a = 1/5 - (1 + u)/4 + u/3
  complex b = 1/4 - (1 + u)/3 + u/2
  complex c = (u^5)*1/5 - (u^4)*(1 + u)/4 + (u^3)*u/3
  complex d = (u^4)*1/4 - (u^3)*(1 + u)/3 + (u^2)*u/2
  complex qa = a*d - b*c
  complex qb = d - b - c
  complex qrad = (sqr(qb) + 4*qa)/(sqr(@branchcut)*(u^10))
  complex p4 = (sqrt(qrad)*@branchcut*(u^5) - qb)/(2*qa)
  complex p = p4^(1/4)
  complex q = p*(1 + c*p4)/(d*p4)
  complex r = u*p
  complex a4 = -0.25*(p + q + r)
  complex a3 = 0.3333333333333333333*(p*q + p*r + q*r)
  complex a2 = -0.5*p*q*r
  z = q
loop:
  z = (((0.2*z + a4)*z + a3)*z + a2)*sqr(z) + p
bailout:
  |z| <= @bailout
default:
  title = "Trail1111"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrail1111"
  seed = #pixel
  branchcut = branchcut
  bailout = bailout
}


Jrail1111 {
; Generic Julia set
init:
  complex u = 1/@seed
  complex a = 1/5 - (1 + u)/4 + u/3
  complex b = 1/4 - (1 + u)/3 + u/2
  complex c = (u^5)*1/5 - (u^4)*(1 + u)/4 + (u^3)*u/3
  complex d = (u^4)*1/4 - (u^3)*(1 + u)/3 + (u^2)*u/2
  complex qa = a*d - b*c
  complex qb = d - b - c
  complex qrad = (sqr(qb) + 4*qa)/(sqr(@branchcut)*(u^10))
  complex p4 = (sqrt(qrad)*@branchcut*(u^5) - qb)/(2*qa)
  complex p = p4^(1/4)
  complex q = p*(1 + c*p4)/(d*p4)
  complex r = u*p
  complex a4 = -0.25*(p + q + r)
  complex a3 = 0.3333333333333333333*(p*q + p*r + q*r)
  complex a2 = -0.5*p*q*r
  z = #pixel*2
loop:
  z = (((0.2*z + a4)*z + a3)*z + a2)*sqr(z) + p
bailout:
  |z| <= @bailout
default:
  title = "Jrail1111"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trail1111"
  branchcut = branchcut
  bailout = bailout
}

Disct1001 {
; Generic Mandelbrot set
init:
  complex u = #pixel
  float hr = real(@hypcent)
  float hi = imag(@hypcent)
  u = ((hr + 1)*u + (hr - 1))/((hr - 1)*u + (hr + 1))
  u = ((hi + 1)*u + flip(hi - 1))/(-flip(hi - 1)*u + (hi + 1))
  if |u| > 1
    u = 1/u
  endif
  complex fu00 = (1.77690860944722, 0)
  complex fu01 = (1.46881047324958, 0)
  complex fu02 = (1.46881047324958, 0)
  complex fu03 = (1.77690860944722, 0)
  complex fu10 = (3.94588866140397, 0)
  complex fu11 = (1.85030181832271, 3.33862554194208)
  complex fu12 = (1.85030181832271, -3.33862554194208)
  complex fu13 = (3.94588866140397, 0)
  complex fu20 = (2.46378306900086, 0)
  complex fu21 = (0, 2.25171645885873)
  complex fu22 = (0, -2.25171645885873)
  complex fu23 = (2.46378306900086, 0)
  complex fu30 = (3.94588866140397, 0)
  complex fu31 = (-1.85030181832271, 3.33862554194208)
  complex fu32 = (-1.85030181832271, -3.33862554194208)
  complex fu33 = (3.94588866140397, 0)
  complex fu40 = (1.77690860944722, 0)
  complex fu41 = (-1.46881047324958, 0)
  complex fu42 = (-1.46881047324958, 0)
  complex fu43 = (1.77690860944722, 0)
  complex fu50 = (3.94588866140397, 0)
  complex fu51 = (-1.85030181832271, -3.33862554194208)
  complex fu52 = (-1.85030181832271, 3.33862554194208)
  complex fu53 = (3.94588866140397, 0)
  complex fu60 = (2.46378306900086, 0)
  complex fu61 = (0, -2.25171645885873)
  complex fu62 = (0, 2.25171645885873)
  complex fu63 = (2.46378306900086, 0)
  complex fu70 = (3.94588866140397, 0)
  complex fu71 = (1.85030181832271, -3.33862554194208)
  complex fu72 = (1.85030181832271, 3.33862554194208)
  complex fu73 = (3.94588866140397, 0)
  complex vu00 = (-7.50400311432317, 0)
  complex vu01 = (-7.43707353330407, 0)
  complex vu02 = (-7.43707353330407, 0)
  complex vu03 = (-7.50400311432317, 0)
  complex vu10 = (-2.77930983550961, 0)
  complex vu11 = (-2.50794536109344, 0.659373359736633)
  complex vu12 = (-2.50794536109344, -0.659373359736633)
  complex vu13 = (-2.77930983550961, 0)
  complex vu20 = (-1.9390184119849, 0)
  complex vu21 = (0, 1.66126229175781)
  complex vu22 = (0, -1.66126229175781)
  complex vu23 = (-1.9390184119849, 0)
  complex vu30 = (-2.77930983550961, 0)
  complex vu31 = (2.50794536109346, 0.659373359736601)
  complex vu32 = (2.50794536109346, -0.659373359736601)
  complex vu33 = (-2.77930983550961, 0)
  complex vu40 = (-7.50400311432317, 0)
  complex vu41 = (7.43707353330408, 0)
  complex vu42 = (7.43707353330408, 0)
  complex vu43 = (-7.50400311432317, 0)
  complex vu50 = (-2.77930983550961, 0)
  complex vu51 = (2.50794536109343, -0.659373359736629)
  complex vu52 = (2.50794536109343, 0.659373359736629)
  complex vu53 = (-2.77930983550961, 0)
  complex vu60 = (-1.93901841198489, 0)
  complex vu61 = (0, -1.66126229175781)
  complex vu62 = (0, 1.66126229175781)
  complex vu63 = (-1.93901841198489, 0)
  complex vu70 = (-2.7793098355096, 0)
  complex vu71 = (-2.50794536109342, -0.659373359736614)
  complex vu72 = (-2.50794536109342, 0.659373359736614)
  complex vu73 = (-2.7793098355096, 0)
  complex umata = (1.42840693882772, 0.427063077513297)
  complex umatb = (-0.755537674043285, -0.807398339215268)
  complex umatc = (-0.755537674043285, 0.807398339215268)
  complex umatd = (1.42840693882772, -0.427063077513297)
  complex ffun = (0.768941951305078, 0.755734340081718)
  float ffnm = 0.1624061172
  complex vfun = (0.921938510567301, 0.708458141083453)
  float vfnm = 0.3518835549
  bool better = true
  complex t = 0
  while better
    better = false
    t = (fu00*u + fu01)/(fu02*u + fu03)
    if |t| < |u|
      better = true
      u = t
    endif
    t = (fu10*u + fu11)/(fu12*u + fu13)
    if |u + ffun| < ffnm
      better = true
      u = t
    endif
    t = (fu20*u + fu21)/(fu22*u + fu23)
    if |t| < |u|
      better = true
      u = t
    endif
    t = (fu30*u + fu31)/(fu32*u + fu33)
    if |u - conj(ffun)| < ffnm
      better = true
      u = t
    endif
    t = (fu40*u + fu41)/(fu42*u + fu43)
    if |t| < |u|
      better = true
      u = t
    endif
    t = (fu50*u + fu51)/(fu52*u + fu53)
    if |u - ffun| < ffnm
      better = true
      u = t
    endif
    t = (fu60*u + fu61)/(fu62*u + fu63)
    if |t| < |u|
      better = true
      u = t
    endif
    t = (fu70*u + fu71)/(fu72*u + fu73)
    if |u + conj(ffun)| < ffnm
      better = true
      u = t
    endif
  endwhile
  complex v = (umata*u + umatb)/(umatc*u + umatd)
  better = true
  while better
    better = false
    t = (vu00*v + vu01)/(vu02*v + vu03)
    if |t| < |v|
      better = true
      v = t
    endif
    t = (vu10*v + vu11)/(vu12*v + vu13)
    if |v + conj(vfun)| < vfnm
      better = true
      v = t
    endif
    t = (vu20*v + vu21)/(vu22*v + vu23)
    if |t| < |v|
      better = true
      v = t
    endif
    t = (vu30*v + vu31)/(vu32*v + vu33)
    if |v - vfun| < vfnm
      better = true
      v = t
    endif
    t = (vu40*v + vu41)/(vu42*v + vu43)
    if |t| < |v|
      better = true
      v = t
    endif
    t = (vu50*v + vu51)/(vu52*v + vu53)
    if |v - conj(vfun)| < vfnm
      better = true
      v = t
    endif
    t = (vu60*v + vu61)/(vu62*v + vu63)
    if |t| < |v|
      better = true
      v = t
    endif
    t = (vu70*v + vu71)/(vu72*v + vu73)
    if |v + vfun| < vfnm
      better = true
      v = t
    endif
  endwhile
  if |v| > |u|
    complex uu = u*u
    complex sz = \
      ((((((((((((((((((((((((((((((-107.899052277213*uu + \
       21.2770763932456)*uu + \
       123.557554926527)*uu + \
       34.878284584795)*uu + \
       -76.1887474600412)*uu + \
       -47.8814482909812)*uu + \
       23.8324277528302)*uu + \
       39.040519155879)*uu + \
       9.42171037859023)*uu + \
       -20.5680212888404)*uu + \
       -9.05777474767476)*uu + \
       10.8937051146504)*uu + \
       6.42065776554998)*uu + \
       -11.3916063653235)*uu + \
       -4.31250669769003)*uu + \
       7.23179734042934)*uu + \
       7.32151528876689)*uu + \
       0.0878771623009697)*uu + \
       -10.4994277381963)*uu + \
       -5.29496565656728)*uu + \
       12.4723716109794)*uu + \
       5.78113558762366)*uu + \
       -3.09586518741821)*uu + \
       -3.72979846852408)*uu + \
       -2.8982466685946)*uu + \
       3.92669738155489)*uu + \
       3.80430717215926)*uu + \
       -0.155685492779724)*uu + \
       -2.46037116317731)*uu + \
       0.0386530703521177)*uu + \
       0.242336927686212)*uu + \
       0.337465527735398
    complex nz = \
      ((((-2.56824559038471*uu + \
       -1.2753190607584)*uu + \
       3.16233893307257)*uu + \
       0.732072552064355)*uu + \
       -0.532580346636843)*uu + \
       1
    complex dz = \
      ((((3.07009900368905*uu + \
       0.933171198790568)*uu + \
       -3.43342914111542)*uu + \
       -0.532580346636843)*uu + \
       1)*uu
    complex sw = \
      (((((((((((((((((((((((((((((((3555.78069325637*uu + \
       9174.78283666175)*uu + \
       2029.07777370326)*uu + \
       -4698.25741013124)*uu + \
       -3929.32308893743)*uu + \
       1445.97750746116)*uu + \
       3006.04573970273)*uu + \
       59.8212021887664)*uu + \
       -1518.62229340824)*uu + \
       -463.990910157965)*uu + \
       642.572940061848)*uu + \
       415.053238113246)*uu + \
       -327.893167847835)*uu + \
       -384.802823768269)*uu + \
       209.843856335763)*uu + \
       359.094423662056)*uu + \
       -67.3864301762284)*uu + \
       -293.51734738998)*uu + \
       -81.4170479138018)*uu + \
       126.072210900492)*uu + \
       154.131534422182)*uu + \
       -24.4616407845213)*uu + \
       -130.305391189651)*uu + \
       -25.0401437192133)*uu + \
       53.8434666456734)*uu + \
       29.3142950063743)*uu + \
       0.0485141455730172)*uu + \
       -22.0620261460773)*uu + \
       -10.3383118018955)*uu + \
       6.77608111273922)*uu + \
       3.32101640138696)*uu + \
       -0.315227932252338)*u
    complex nw = \
      (((((((((((37.1640947580495*uu + \
       25.2366970146757)*uu + \
       -79.2348889251695)*uu + \
       -39.336002799837)*uu + \
       72.769261866207)*uu + \
       15.4988717415633)*uu + \
       -45.2051250201327)*uu + \
       4.79811103250217)*uu + \
       26.875698337622)*uu + \
       -4.36895133682953)*uu + \
       -11.8635126784192)*uu + \
       -0.487787046566006)*uu + \
       1
    complex dw = \
      ((((((((((-16.5150902671358*uu + \
       -12.5496006514766)*uu + \
       43.3130286369739)*uu + \
       28.0695603199555)*uu + \
       -47.3063360019564)*uu + \
       -23.8657389027764)*uu + \
       26.998716697107)*uu + \
       9.14288441064084)*uu + \
       -8.05174442974391)*uu + \
       -1.33145086659211)*uu + \
       1)*uu*uu*u
  else
    complex vv = v*v
    complex sz = \
      ((((((((((((((((((((((((((((((-62.4142684201291*vv + \
       -24.4501359821071)*vv + \
       24.9667464256093)*vv + \
       55.9134526879858)*vv + \
       0.861712635046834)*vv + \
       -44.1996662928199)*vv + \
       -31.0932383175414)*vv + \
       16.5587830761816)*vv + \
       21.3477545172581)*vv + \
       9.15209897860366)*vv + \
       -11.816269085359)*vv + \
       -14.1189260861883)*vv + \
       2.25234505972364)*vv + \
       17.1917759703915)*vv + \
       0.959639718089691)*vv + \
       -6.18554879409297)*vv + \
       -10.0756614899533)*vv + \
       -0.170923360334278)*vv + \
       5.48048121957309)*vv + \
       7.38528123614971)*vv + \
       -3.20728461877661)*vv + \
       -3.74427890637652)*vv + \
       -0.946307781751826)*vv + \
       0.791698298683063)*vv + \
       -0.133793544014046)*vv + \
       0.974006735151753)*vv + \
       -2.81024562545752)*vv + \
       -0.178804017105037)*vv + \
       1.85856061196747)*vv + \
       1.20293852755071)*vv + \
       0.23875336908879)*vv + \
       1.25680374453813
    complex nz = \
      (((((((-32.1646494392229*vv + \
       67.0799646778823)*vv + \
       -31.1827814288078)*vv + \
       5.78887758712353)*vv + \
       -35.94865920118)*vv + \
       17.7836740854269)*vv + \
       23.3043764521405)*vv + \
       -15.3348776972945)*vv
    complex dz = \
      (((((((16.8395759388293*vv + \
       -36.299982458833)*vv + \
       17.9611398639406)*vv + \
       1.97417157772669)*vv + \
       7.9776240015738)*vv + \
       -8.85768229233788)*vv + \
       -0.389287734944832)*vv + \
       0.06051432707662)*vv + \
       1
    complex sw = \
      (((((((((((((((((((((((((((((((-4588.39425946336*vv + \
       -638.028878742982)*vv + \
       2926.6271307215)*vv + \
       2152.42986111644)*vv + \
       -1133.18980867301)*vv + \
       -1770.43568957182)*vv + \
       -326.336065212859)*vv + \
       996.624479004599)*vv + \
       893.114143000207)*vv + \
       -42.4102681844128)*vv + \
       -826.16752834257)*vv + \
       -290.915857805946)*vv + \
       279.471671930001)*vv + \
       304.282599876931)*vv + \
       -20.0082437613319)*vv + \
       -155.862003016844)*vv + \
       -143.314264270139)*vv + \
       77.2973695495412)*vv + \
       131.155409882033)*vv + \
       24.7131392048309)*vv + \
       -74.9750389466605)*vv + \
       -28.5833919478334)*vv + \
       -8.81570321911416)*vv + \
       30.7433882288918)*vv + \
       16.2933118995542)*vv + \
       -7.7092253784646)*vv + \
       -13.2179549391542)*vv + \
       5.08259886063704)*vv + \
       0.655017515069468)*vv + \
       -0.322521671055053)*vv + \
       -0.434957426348914)*vv + \
       -1.71590514351575)*v
    complex nw = \
      (((((((((((((((((((-1828.72142791126*vv + \
       12560.4666412313)*vv + \
       -34496.9609357505)*vv + \
       47614.274908282)*vv + \
       -34314.4635749314)*vv + \
       16600.6038334992)*vv + \
       -17194.056110468)*vv + \
       18214.4803937559)*vv + \
       -5825.9381730092)*vv + \
       -4217.19020198348)*vv + \
       2925.71204970639)*vv + \
       1726.73491114304)*vv + \
       -1332.45112129072)*vv + \
       -5073.25506475846)*vv + \
       9750.30323439105)*vv + \
       -7196.76526038431)*vv + \
       2084.68379613108)*vv + \
       254.292308376439)*vv + \
       -310.093045112662)*vv + \
       58.4753135277179)*v
    complex dw = \
      (((((((((((((((((((1163.6647447058*vv + \
       -6271.09167924206)*vv + \
       13241.559785214)*vv + \
       -13334.6283268819)*vv + \
       7183.05738965072)*vv + \
       -6214.10795044865)*vv + \
       9142.28222037823)*vv + \
       -6189.68943816696)*vv + \
       1558.40968010435)*vv + \
       -1798.44406773222)*vv + \
       2292.32500964001)*vv + \
       -644.465585190844)*vv + \
       25.8275654912191)*vv + \
       -351.701784979822)*vv + \
       181.215008149509)*vv + \
       19.6546841043565)*vv + \
       18.216807213465)*vv + \
       -22.2324770500086)*vv + \
       -0.966353117772193)*vv + \
       0.151285817691546)*vv + \
       1
  endif
  sz = 0.0236200184650903*(sz + nz/dz)
  sw = 8.57433765636572e-005*(sw + nw/dw)
  sz = sz - 0.2345841323737324
  sw = 45.8105095272213*sw
  sw = sw/(sz*sqr(sz))
  complex s = 1/sz + 4.2940434292888333
  if @radical
    complex qrad = sqrt(((((sqr(s) - 30)*s + 54)*s - 15)*s - 18)*s + 9)
    if |sw - qrad| < |sw + qrad|
      sw = qrad
    else
      sw = -qrad
    endif
  endif
  t = ((5*sqr(s) - 3)*s + 3 + sw)/(6*sqr(s))
  complex a0 = s
  complex a2 = -1.5*t
  complex p = (t - a0)/(1 + a2)
  z = t
loop:
  z = (z + a2)*sqr(z)*p + a0
bailout:
  |z| <= @bailout
default:
  title = "Disct1001"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param hypcent
    caption = "Hyperbolic Translation"
    default = (1,1)
    hint = "Move the origin around by a horizontal move followed \
            by vertical move. (1, 4.715499527859587), (1, 1), \
            (3.245719082696797, 1),  (14.94107664762724, 4.715499527859587) \
            center 4 of 6 Weierstrass points."
  endparam
  param radical
    caption = "Radical"
    default = false
    hint = "From a purist standpoint this is unnecessary.  It helps \
            coherence on zooms deeper than 1e8."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128000000.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jisct1001"
  seed = #pixel
  hypcent = hypcent
  radical = radical
  bailout = bailout
}

Jisct1001 {
; Generic Mandelbrot set
init:
  complex u = @seed
  float hr = real(@hypcent)
  float hi = imag(@hypcent)
  u = ((hr + 1)*u + (hr - 1))/((hr - 1)*u + (hr + 1))
  u = ((hi + 1)*u + flip(hi - 1))/(-flip(hi - 1)*u + (hi + 1))
  if |u| > 1
    u = 1/u
  endif
  complex fu00 = (1.77690860944722, 0)
  complex fu01 = (1.46881047324958, 0)
  complex fu02 = (1.46881047324958, 0)
  complex fu03 = (1.77690860944722, 0)
  complex fu10 = (3.94588866140397, 0)
  complex fu11 = (1.85030181832271, 3.33862554194208)
  complex fu12 = (1.85030181832271, -3.33862554194208)
  complex fu13 = (3.94588866140397, 0)
  complex fu20 = (2.46378306900086, 0)
  complex fu21 = (0, 2.25171645885873)
  complex fu22 = (0, -2.25171645885873)
  complex fu23 = (2.46378306900086, 0)
  complex fu30 = (3.94588866140397, 0)
  complex fu31 = (-1.85030181832271, 3.33862554194208)
  complex fu32 = (-1.85030181832271, -3.33862554194208)
  complex fu33 = (3.94588866140397, 0)
  complex fu40 = (1.77690860944722, 0)
  complex fu41 = (-1.46881047324958, 0)
  complex fu42 = (-1.46881047324958, 0)
  complex fu43 = (1.77690860944722, 0)
  complex fu50 = (3.94588866140397, 0)
  complex fu51 = (-1.85030181832271, -3.33862554194208)
  complex fu52 = (-1.85030181832271, 3.33862554194208)
  complex fu53 = (3.94588866140397, 0)
  complex fu60 = (2.46378306900086, 0)
  complex fu61 = (0, -2.25171645885873)
  complex fu62 = (0, 2.25171645885873)
  complex fu63 = (2.46378306900086, 0)
  complex fu70 = (3.94588866140397, 0)
  complex fu71 = (1.85030181832271, -3.33862554194208)
  complex fu72 = (1.85030181832271, 3.33862554194208)
  complex fu73 = (3.94588866140397, 0)
  complex vu00 = (-7.50400311432317, 0)
  complex vu01 = (-7.43707353330407, 0)
  complex vu02 = (-7.43707353330407, 0)
  complex vu03 = (-7.50400311432317, 0)
  complex vu10 = (-2.77930983550961, 0)
  complex vu11 = (-2.50794536109344, 0.659373359736633)
  complex vu12 = (-2.50794536109344, -0.659373359736633)
  complex vu13 = (-2.77930983550961, 0)
  complex vu20 = (-1.9390184119849, 0)
  complex vu21 = (0, 1.66126229175781)
  complex vu22 = (0, -1.66126229175781)
  complex vu23 = (-1.9390184119849, 0)
  complex vu30 = (-2.77930983550961, 0)
  complex vu31 = (2.50794536109346, 0.659373359736601)
  complex vu32 = (2.50794536109346, -0.659373359736601)
  complex vu33 = (-2.77930983550961, 0)
  complex vu40 = (-7.50400311432317, 0)
  complex vu41 = (7.43707353330408, 0)
  complex vu42 = (7.43707353330408, 0)
  complex vu43 = (-7.50400311432317, 0)
  complex vu50 = (-2.77930983550961, 0)
  complex vu51 = (2.50794536109343, -0.659373359736629)
  complex vu52 = (2.50794536109343, 0.659373359736629)
  complex vu53 = (-2.77930983550961, 0)
  complex vu60 = (-1.93901841198489, 0)
  complex vu61 = (0, -1.66126229175781)
  complex vu62 = (0, 1.66126229175781)
  complex vu63 = (-1.93901841198489, 0)
  complex vu70 = (-2.7793098355096, 0)
  complex vu71 = (-2.50794536109342, -0.659373359736614)
  complex vu72 = (-2.50794536109342, 0.659373359736614)
  complex vu73 = (-2.7793098355096, 0)
  complex umata = (1.42840693882772, 0.427063077513297)
  complex umatb = (-0.755537674043285, -0.807398339215268)
  complex umatc = (-0.755537674043285, 0.807398339215268)
  complex umatd = (1.42840693882772, -0.427063077513297)
  complex ffun = (0.768941951305078, 0.755734340081718)
  float ffnm = 0.1624061172
  complex vfun = (0.921938510567301, 0.708458141083453)
  float vfnm = 0.3518835549
  bool better = true
  complex t = 0
  while better
    better = false
    t = (fu00*u + fu01)/(fu02*u + fu03)
    if |t| < |u|
      better = true
      u = t
    endif
    t = (fu10*u + fu11)/(fu12*u + fu13)
    if |u + ffun| < ffnm
      better = true
      u = t
    endif
    t = (fu20*u + fu21)/(fu22*u + fu23)




    if |t| < |u|
      better = true
      u = t
    endif
    t = (fu30*u + fu31)/(fu32*u + fu33)
    if |u - conj(ffun)| < ffnm
      better = true
      u = t
    endif
    t = (fu40*u + fu41)/(fu42*u + fu43)
    if |t| < |u|
      better = true
      u = t
    endif
    t = (fu50*u + fu51)/(fu52*u + fu53)
    if |u - ffun| < ffnm
      better = true
      u = t
    endif
    t = (fu60*u + fu61)/(fu62*u + fu63)
    if |t| < |u|
      better = true
      u = t
    endif
    t = (fu70*u + fu71)/(fu72*u + fu73)
    if |u + conj(ffun)| < ffnm
      better = true
      u = t
    endif
  endwhile
  complex v = (umata*u + umatb)/(umatc*u + umatd)
  better = true
  while better
    better = false
    t = (vu00*v + vu01)/(vu02*v + vu03)
    if |t| < |v|
      better = true
      v = t
    endif
    t = (vu10*v + vu11)/(vu12*v + vu13)
    if |v + conj(vfun)| < vfnm
      better = true
      v = t
    endif
    t = (vu20*v + vu21)/(vu22*v + vu23)
    if |t| < |v|
      better = true
      v = t
    endif
    t = (vu30*v + vu31)/(vu32*v + vu33)
    if |v - vfun| < vfnm
      better = true
      v = t
    endif
    t = (vu40*v + vu41)/(vu42*v + vu43)
    if |t| < |v|
      better = true
      v = t
    endif
    t = (vu50*v + vu51)/(vu52*v + vu53)
    if |v - conj(vfun)| < vfnm
      better = true
      v = t
    endif
    t = (vu60*v + vu61)/(vu62*v + vu63)
    if |t| < |v|
      better = true
      v = t
    endif
    t = (vu70*v + vu71)/(vu72*v + vu73)
    if |v + vfun| < vfnm
      better = true
      v = t
    endif
  endwhile
  if |v| > |u|
    complex uu = u*u
    complex sz = \
      ((((((((((((((((((((((((((((((-107.899052277213*uu + \
       21.2770763932456)*uu + \
       123.557554926527)*uu + \
       34.878284584795)*uu + \
       -76.1887474600412)*uu + \
       -47.8814482909812)*uu + \
       23.8324277528302)*uu + \
       39.040519155879)*uu + \
       9.42171037859023)*uu + \
       -20.5680212888404)*uu + \

       -9.05777474767476)*uu + \
       10.8937051146504)*uu + \
       6.42065776554998)*uu + \
       -11.3916063653235)*uu + \
       -4.31250669769003)*uu + \
       7.23179734042934)*uu + \
       7.32151528876689)*uu + \
       0.0878771623009697)*uu + \
       -10.4994277381963)*uu + \
       -5.29496565656728)*uu + \
       12.4723716109794)*uu + \
       5.78113558762366)*uu + \
       -3.09586518741821)*uu + \
       -3.72979846852408)*uu + \
       -2.8982466685946)*uu + \
       3.92669738155489)*uu + \
       3.80430717215926)*uu + \
       -0.155685492779724)*uu + \
       -2.46037116317731)*uu + \
       0.0386530703521177)*uu + \
       0.242336927686212)*uu + \
       0.337465527735398
    complex nz = \
      ((((-2.56824559038471*uu + \
       -1.2753190607584)*uu + \
       3.16233893307257)*uu + \
       0.732072552064355)*uu + \
       -0.532580346636843)*uu + \
       1
    complex dz = \
      ((((3.07009900368905*uu + \
       0.933171198790568)*uu + \
       -3.43342914111542)*uu + \
       -0.532580346636843)*uu + \
       1)*uu
    complex sw = \
      (((((((((((((((((((((((((((((((3555.78069325637*uu + \
       9174.78283666175)*uu + \
       2029.07777370326)*uu + \
       -4698.25741013124)*uu + \
       -3929.32308893743)*uu + \
       1445.97750746116)*uu + \
       3006.04573970273)*uu + \
       59.8212021887664)*uu + \
       -1518.62229340824)*uu + \
       -463.990910157965)*uu + \
       642.572940061848)*uu + \
       415.053238113246)*uu + \
       -327.893167847835)*uu + \
       -384.802823768269)*uu + \
       209.843856335763)*uu + \
       359.094423662056)*uu + \
       -67.3864301762284)*uu + \
       -293.51734738998)*uu + \
       -81.4170479138018)*uu + \
       126.072210900492)*uu + \
       154.131534422182)*uu + \
       -24.4616407845213)*uu + \
       -130.305391189651)*uu + \
       -25.0401437192133)*uu + \
       53.8434666456734)*uu + \
       29.3142950063743)*uu + \
       0.0485141455730172)*uu + \
       -22.0620261460773)*uu + \
       -10.3383118018955)*uu + \
       6.77608111273922)*uu + \
       3.32101640138696)*uu + \
       -0.315227932252338)*u
    complex nw = \
      (((((((((((37.1640947580495*uu + \
       25.2366970146757)*uu + \
       -79.2348889251695)*uu + \
       -39.336002799837)*uu + \
       72.769261866207)*uu + \
       15.4988717415633)*uu + \
       -45.2051250201327)*uu + \
       4.79811103250217)*uu + \
       26.875698337622)*uu + \
       -4.36895133682953)*uu + \
       -11.8635126784192)*uu + \
       -0.487787046566006)*uu + \
       1
    complex dw = \
      ((((((((((-16.5150902671358*uu + \
       -12.5496006514766)*uu + \
       43.3130286369739)*uu + \
       28.0695603199555)*uu + \
       -47.3063360019564)*uu + \
       -23.8657389027764)*uu + \
       26.998716697107)*uu + \
       9.14288441064084)*uu + \
       -8.05174442974391)*uu + \
       -1.33145086659211)*uu + \
       1)*uu*uu*u
  else
    complex vv = v*v
    complex sz = \
      ((((((((((((((((((((((((((((((-62.4142684201291*vv + \
       -24.4501359821071)*vv + \
       24.9667464256093)*vv + \
       55.9134526879858)*vv + \
       0.861712635046834)*vv + \
       -44.1996662928199)*vv + \
       -31.0932383175414)*vv + \
       16.5587830761816)*vv + \
       21.3477545172581)*vv + \
       9.15209897860366)*vv + \
       -11.816269085359)*vv + \
       -14.1189260861883)*vv + \
       2.25234505972364)*vv + \
       17.1917759703915)*vv + \
       0.959639718089691)*vv + \
       -6.18554879409297)*vv + \
       -10.0756614899533)*vv + \
       -0.170923360334278)*vv + \
       5.48048121957309)*vv + \
       7.38528123614971)*vv + \
       -3.20728461877661)*vv + \
       -3.74427890637652)*vv + \
       -0.946307781751826)*vv + \
       0.791698298683063)*vv + \
       -0.133793544014046)*vv + \
       0.974006735151753)*vv + \
       -2.81024562545752)*vv + \
       -0.178804017105037)*vv + \
       1.85856061196747)*vv + \

       1.20293852755071)*vv + \
       0.23875336908879)*vv + \
       1.25680374453813
    complex nz = \
      (((((((-32.1646494392229*vv + \
       67.0799646778823)*vv + \
       -31.1827814288078)*vv + \
       5.78887758712353)*vv + \
       -35.94865920118)*vv + \
       17.7836740854269)*vv + \
       23.3043764521405)*vv + \
       -15.3348776972945)*vv
    complex dz = \
      (((((((16.8395759388293*vv + \
       -36.299982458833)*vv + \
       17.9611398639406)*vv + \
       1.97417157772669)*vv + \
       7.9776240015738)*vv + \
       -8.85768229233788)*vv + \
       -0.389287734944832)*vv + \
       0.06051432707662)*vv + \
       1
    complex sw = \
      (((((((((((((((((((((((((((((((-4588.39425946336*vv + \
       -638.028878742982)*vv + \
       2926.6271307215)*vv + \
       2152.42986111644)*vv + \
       -1133.18980867301)*vv + \
       -1770.43568957182)*vv + \
       -326.336065212859)*vv + \
       996.624479004599)*vv + \
       893.114143000207)*vv + \
       -42.4102681844128)*vv + \
       -826.16752834257)*vv + \
       -290.915857805946)*vv + \
       279.471671930001)*vv + \
       304.282599876931)*vv + \
       -20.0082437613319)*vv + \
       -155.862003016844)*vv + \
       -143.314264270139)*vv + \
       77.2973695495412)*vv + \
       131.155409882033)*vv + \
       24.7131392048309)*vv + \
       -74.9750389466605)*vv + \
       -28.5833919478334)*vv + \
       -8.81570321911416)*vv + \
       30.7433882288918)*vv + \
       16.2933118995542)*vv + \
       -7.7092253784646)*vv + \
       -13.2179549391542)*vv + \
       5.08259886063704)*vv + \
       0.655017515069468)*vv + \
       -0.322521671055053)*vv + \
       -0.434957426348914)*vv + \
       -1.71590514351575)*v
    complex nw = \
      (((((((((((((((((((-1828.72142791126*vv + \
       12560.4666412313)*vv + \
       -34496.9609357505)*vv + \
       47614.274908282)*vv + \
       -34314.4635749314)*vv + \
       16600.6038334992)*vv + \
       -17194.056110468)*vv + \
       18214.4803937559)*vv + \
       -5825.9381730092)*vv + \

       -4217.19020198348)*vv + \
       2925.71204970639)*vv + \
       1726.73491114304)*vv + \
       -1332.45112129072)*vv + \
       -5073.25506475846)*vv + \
       9750.30323439105)*vv + \
       -7196.76526038431)*vv + \
       2084.68379613108)*vv + \
       254.292308376439)*vv + \
       -310.093045112662)*vv + \
       58.4753135277179)*v
    complex dw = \
      (((((((((((((((((((1163.6647447058*vv + \
       -6271.09167924206)*vv + \
       13241.559785214)*vv + \
       -13334.6283268819)*vv + \
       7183.05738965072)*vv + \
       -6214.10795044865)*vv + \
       9142.28222037823)*vv + \
       -6189.68943816696)*vv + \
       1558.40968010435)*vv + \
       -1798.44406773222)*vv + \
       2292.32500964001)*vv + \
       -644.465585190844)*vv + \
       25.8275654912191)*vv + \
       -351.701784979822)*vv + \
       181.215008149509)*vv + \
       19.6546841043565)*vv + \
       18.216807213465)*vv + \
       -22.2324770500086)*vv + \
       -0.966353117772193)*vv + \
       0.151285817691546)*vv + \
       1
  endif
  sz = 0.0236200184650903*(sz + nz/dz)
  sw = 8.57433765636572e-005*(sw + nw/dw)
  sz = sz - 0.2345841323737324
  sw = 45.8105095272213*sw
  sw = sw/(sz*sqr(sz))
  complex s = 1/sz + 4.2940434292888333
  if @radical
    complex qrad = sqrt(((((sqr(s) - 30)*s + 54)*s - 15)*s - 18)*s + 9)
    if |sw - qrad| < |sw + qrad|
      sw = qrad
    else
      sw = -qrad
    endif
  endif
  t = ((5*sqr(s) - 3)*s + 3 + sw)/(6*sqr(s))
  complex a0 = s
  complex a2 = -1.5*t
  complex p = (t - a0)/(1 + a2)
  z = #pixel
loop:
  z = (z + a2)*sqr(z)*p + a0
bailout:
  |z| <= @bailout
default:
  title = "Jisct1001"
  center = (0, 0)
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param hypcent
    caption = "Hyperbolic Translation"
    default = (1,1)
    hint = "Move the origin around by a horizontal move followed \
            by vertical move. (1, 4.715499527859587), (1, 1), \
            (3.245719082696797, 1),  (14.94107664762724, 4.715499527859587) \
            center 4 of 6 Weierstrass points."
  endparam
  param radical
    caption = "Radical"
    default = false
    hint = "From a purist standpoint this is unnecessary.  It helps \
            coherence on zooms deeper than 1e8."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128000000.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Disct1001"
  hypcent = hypcent
  radical = radical
  bailout = bailout
}

Trail1001 {
; Generic Mandelbrot set
init:
  complex u = 1/#pixel
  complex t = u
  if @unwrap || @unwrap3
    complex z0 = 1/(-0.396605040933576095, -0.360564887026954119)
    complex z1 = 1/(-0.396605040933576095, 0.360564887026954119)
    complex z2 = 1/(0.160623225673253248, 0)
    complex z3 = 1/(0.767119262655986455, 0)
    complex z4 = 1/(1.16021692001170013, 0)
    complex z5 = 1/(2.70525067352621236, 0)
    if @br0 == 0
      complex root0 = z0
    elseif @br0 == 1
      complex root0 = z1
    elseif @br0 == 2
      complex root0 = z2
    elseif @br0 == 3
      complex root0 = z3
    elseif @br0 == 4
      complex root0 = z4
    else
      complex root0 = z5
    endif
    if @br1 == 0
      complex root1 = z0
    elseif @br1 == 1
      complex root1 = z1
    elseif @br1 == 2
      complex root1 = z2
    elseif @br1 == 3
      complex root1 = z3
    elseif @br1 == 4
      complex root1 = z4
    else
      complex root1 = z5
    endif
    if @br2 == 0
      complex root2 = z0
    elseif @br2 == 1
      complex root2 = z1
    elseif @br2 == 2
      complex root2 = z2
    elseif @br2 == 3
      complex root2 = z3
    elseif @br2 == 4
      complex root2 = z4
    else
      complex root2 = z5
    endif
    t = 1
    if @unwrap3
      complex m = (root0 + root1 - 2*root2)/2
      complex n = sqr(root0 - root1)/16
      t = u + (4*n - sqr(m))/(16*u)
      u = u - (4*n - sqr(m))/(16*u) - 0.5*m
    endif
    t = (u - sqr(root0 - root1)/(16*u))*t
    u = u + sqr(root0 - root1)/(16*u) + 0.5*(root0 + root1)
  endif
  complex a = 1/3 - u/2
  complex b = 1/2 - u
  complex c = (u^3)/3 - (u^3)/2
  complex d = (u^2)/2 - (u^2)
  complex qa = a*d - b*c
  complex qb = d - b - c
  if @unwrap3
    complex qrad = (sqr(qb) + 4*qa)/(sqr(@branchcut)*sqr(u)*sqr(t))
    complex p4 = (sqrt(qrad)*@branchcut*u*t - qb)/(2*qa)
  else
    complex qrad = (sqr(qb) + 4*qa)/(sqr(@branchcut)*(u^4)*sqr(t))
    complex p4 = (sqrt(qrad)*@branchcut*(u^2)*t - qb)/(2*qa)
  endif
  complex p = p4^(1/2)
  complex q = p*(1 + c*p4)/(d*p4)
  complex r = u*p
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*(q + r)
  complex a1 = q*r
  z = q
  if @showbranch && (real(qrad) < -10*abs(imag(qrad)))
    z = 1e15
  endif
loop:
  z = ((a3*z + a2)*z + a1)*z + p
bailout:
  |z| <= @bailout
default:
  title = "Trail1001"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this parametization. Use (-1,0) \
            to see the other sheet."
  endparam
  param unwrap
    caption = "Unwrap"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps two and duplicates the rest."
  endparam
  param unwrap3
    caption = "Unwrap3"
    default = false
    hint = "There are six branch points to this parametization. This \

            unwraps three and quadruples the rest."
  endparam
  param showbranch
    caption = "Show branches"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps two and duplicates the rest."
  endparam
  param br0
    caption = "Unwrap Point"
    default = 0
    min = 0
    max = 5
    hint = "Choice of branch point to unwrap.  Make two choices \
            different."
  endparam
  param br1
    caption = "Unwrap Point"
    default = 1
    min = 0
    max = 5
    hint = "Choice of branch point to unwrap.  Make two choices \
            different."
  endparam
  param br2
    caption = "Unwrap Point 3"
    default = 2
    min = 0
    max = 5
    hint = "Choice of branch point to unwrap.  Make third choice \
            different."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jrail1001"
  seed = #pixel
  branchcut = branchcut
  unwrap = unwrap
  unwrap3 = unwrap3
  br0 = br0
  br1 = br1
  br2 = br2
  bailout = bailout
}

Jrail1001 {
; Generic Julia set
init:
  complex u = 1/@seed
  complex t = u
  if @unwrap || @unwrap3
    complex z0 = 1/(-0.396605040933576095, -0.360564887026954119)
    complex z1 = 1/(-0.396605040933576095, 0.360564887026954119)
    complex z2 = 1/(0.160623225673253248, 0)
    complex z3 = 1/(0.767119262655986455, 0)
    complex z4 = 1/(1.16021692001170013, 0)
    complex z5 = 1/(2.70525067352621236, 0)
    if @br0 == 0
      complex root0 = z0
    elseif @br0 == 1
      complex root0 = z1
    elseif @br0 == 2
      complex root0 = z2
    elseif @br0 == 3
      complex root0 = z3
    elseif @br0 == 4
      complex root0 = z4
    else
      complex root0 = z5
    endif
    if @br1 == 0
      complex root1 = z0
    elseif @br1 == 1
      complex root1 = z1
    elseif @br1 == 2
      complex root1 = z2
    elseif @br1 == 3
      complex root1 = z3
    elseif @br1 == 4
      complex root1 = z4
    else
      complex root1 = z5
    endif
    if @br2 == 0
      complex root2 = z0
    elseif @br2 == 1
      complex root2 = z1
    elseif @br2 == 2
      complex root2 = z2
    elseif @br2 == 3
      complex root2 = z3
    elseif @br2 == 4
      complex root2 = z4
    else
      complex root2 = z5
    endif
    t = 1
    if @unwrap3
      complex m = (root0 + root1 - 2*root2)/2
      complex n = sqr(root0 - root1)/16
      t = u + (4*n - sqr(m))/(16*u)
      u = u - (4*n - sqr(m))/(16*u) - 0.5*m
    endif
    t = (u - sqr(root0 - root1)/(16*u))*t
    u = u + sqr(root0 - root1)/(16*u) + 0.5*(root0 + root1)
  endif
  complex a = 1/3 - u/2
  complex b = 1/2 - u
  complex c = (u^3)/3 - (u^3)/2
  complex d = (u^2)/2 - (u^2)
  complex qa = a*d - b*c
  complex qb = d - b - c
  if @unwrap3
    complex qrad = (sqr(qb) + 4*qa)/(sqr(@branchcut)*sqr(u)*sqr(t))
    complex p4 = (sqrt(qrad)*@branchcut*u*t - qb)/(2*qa)
  else
    complex qrad = (sqr(qb) + 4*qa)/(sqr(@branchcut)*(u^4)*sqr(t))
    complex p4 = (sqrt(qrad)*@branchcut*(u^2)*t - qb)/(2*qa)
  endif
  complex p = p4^(1/2)
  complex q = p*(1 + c*p4)/(d*p4)
  complex r = u*p
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*(q + r)
  complex a1 = q*r
  z = 2*#pixel
loop:
  z = ((a3*z + a2)*z + a1)*z + p
bailout:
  |z| <= @bailout
default:
  title = "Jrail1001"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param unwrap
    caption = "Unwrap"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps two and duplicates the rest."
  endparam
  param unwrap3
    caption = "Unwrap3"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps three and quadruples the rest."
  endparam
  param showbranch
    caption = "Show branches"
    default = false
    hint = "There are six branch points to this parametization. This \
            unwraps two and duplicates the rest."
  endparam
  param br0
    caption = "Unwrap Point"
    default = 0
    min = 0
    max = 5
    hint = "Choice of branch point to unwrap.  Make two choices \
            different."
  endparam
  param br1
    caption = "Unwrap Point"
    default = 1
    min = 0
    max = 5
    hint = "Choice of branch point to unwrap.  Make two choices \
            different."
  endparam
  param br2
    caption = "Unwrap Point 3"
    default = 2
    min = 0
    max = 5
    hint = "Choice of branch point to unwrap.  Make third choice \
            different."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Trail1001"
  branchcut = branchcut
  bailout = bailout
}

Step2to1 {
; Generic Mandelbrot set
init:
  complex pix3 = #pixel*#pixel*#pixel
  complex p = #pixel*(1 + 0.25*pix3)/(1 + 0.3333333333333333333*pix3)
  complex a3 = -0.3333333333333333333*p
  z = p
loop:
  z = (0.25*z + a3)*z*sqr(z) + #pixel
bailout:
  |z| <= @bailout
default:
  title = "Step2to1"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout

    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jtep2to1"
  seed = #pixel
  power = power
  bailout = bailout
}


Jtep2to1 {
; Generic Julia set
init:
  complex pix3 = @seed*@seed*@seed
  complex p = @seed*(1 + 0.25*pix3)/(1 + 0.3333333333333333333*pix3)
  complex a3 = -0.3333333333333333333*p
  z = #pixel
loop:
  z = (0.25*z + a3)*z*sqr(z) + @seed
bailout:
  |z| <= @bailout
default:
  title = "Jtep2to1"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Step2to1"
  power = power
  bailout = bailout
}

Vtrail {
; Generic Mandelbrot set
init:
  complex psq = sqr(#pixel)
  complex a2 = -0.5*psq
  complex a0 = #pixel
  z = a0
loop:
  z = (0.25*sqr(z) + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Vtrail"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:

  type = "Vjrail"
  seed = #pixel
  power = power
  bailout = bailout
}


Vjrail {
; Generic Julia set
init:
  complex psq = sqr(@seed)
  complex a2 = -0.5*psq
  complex a0 = @seed
  z = #pixel
loop:
  z = (0.25*sqr(z) + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Vjrail"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Vtrail"
  power = power
  bailout = bailout
}

Meet21 {
; Generic Mandelbrot set
init:
  complex a3 = 0.3333333333333333333*#pixel*(1 + flip(sqrt(2)))
  z = #pixel
loop:
  z = (0.25*z + a3)*z*sqr(z) + #pixel
bailout:
  |z| <= @bailout
default:
  title = "Meet21"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet21"
  seed = #pixel
  power = power
  bailout = bailout
}


Jeet21 {
; Generic Julia set
init:
  complex a3 = 0.3333333333333333333*@seed*(1 + flip(sqrt(2)))
  z = #pixel
loop:
  z = (0.25*z + a3)*z*sqr(z) + @seed
bailout:
  |z| <= @bailout
default:
  title = "Jeet21"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet21"
  power = power
  bailout = bailout
}

Twostep {
; Generic Mandelbrot set
init:
  complex pix2 = #pixel*#pixel
  complex q = #pixel*(6 + 2*pix2)/(6 + 3*pix2)
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*q
  z = q
loop:
  z = (a3*z + a2)*sqr(z) + #pixel
bailout:
  |z| <= @bailout
default:
  title = "Twostep"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jwostep"
  seed = #pixel
  power = power
  bailout = bailout
}


Jwostep {

; Generic Julia set
init:
  complex pix2 = @seed*@seed
  complex q = @seed*(6 + 2*pix2)/(6 + 3*pix2)
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*q
  z = #pixel
loop:
  z = (a3*z + a2)*sqr(z) + @seed
bailout:
  |z| <= @bailout
default:
  title = "Jwostep"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Twostep"
  power = power
  bailout = bailout
}

Meet10_10_0 {
; Generic Mandelbrot set
init:
  complex st = #pixel
  if @insout
    st = 1/st
  endif
  complex sqst = sqrt(sqr(st) - 0.33333333333333333333)
  complex s = sqst + st
  complex t = sqst - st
  complex a3 = 0.33333333333333333333
  complex a2 = -0.5*(s + t)
  complex a1 = -0.33333333333333333333
  complex q = ((a3*s + a2)*s + a1)*s
  complex r = ((a3*t + a2)*t + a1)*t
  complex pn2 = 2/(q - r)
  complex u = 1 - q*pn2
  complex p = sqrt(pn2)
  a2 = a2*p
  a1 = a1*pn2
  complex a0 = u*p
  z = p
loop:
  z = ((a3*z + a2)*z + a1)*z + a0
bailout:
  |z| <= @bailout
default:
  title = "Meet10_10_0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet10_10_0"
  seed = #pixel
  power = power
  insout = insout
  bailout = bailout
}


Jeet10_10_0 {

; Generic Julia set
init:
  complex st = @seed
  if @insout
    st = 1/st
  endif

  complex sqst = sqrt(sqr(st) - 0.33333333333333333333)
  complex s = sqst + st
  complex t = sqst - st
  complex a3 = 0.33333333333333333333
  complex a2 = -0.5*(s + t)
  complex a1 = -0.33333333333333333333
  complex q = ((a3*s + a2)*s + a1)*s
  complex r = ((a3*t + a2)*t + a1)*t
  complex pn2 = 2/(q - r)
  complex u = 1 - q*pn2
  complex p = sqrt(pn2)
  a2 = a2*p
  a1 = a1*pn2
  complex a0 = u*p
  z = 2*#pixel
loop:
  z = ((a3*z + a2)*z + a1)*z + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet10_10_0"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet10_10_0"
  power = power
  bailout = bailout
}

Meet100_1_0 {
; Generic Mandelbrot set
init:
  complex u = 1/#pixel - 1
  complex uu = sqr(u)
  complex u3i = 1/((2*u - 3)*uu + 1)
  complex s = ((2*uu - 3*u)*uu + 1.5)*u3i
  complex p = sqrt((9 - 6*u)*u3i)
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*p
  complex a0 = s*p
  z = a0
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Meet100_1_0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)

    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet100_1_0"
  seed = #pixel
  power = power
  bailout = bailout
}


Jeet100_1_0 {

; Generic Julia set
init:
  complex u = 1/@seed - 1
  complex uu = sqr(u)
  complex u3i = 1/((2*u - 3)*uu + 1)
  complex s = ((2*uu - 3*u)*uu + 1.5)*u3i
  complex p = sqrt((9 - 6*u)*u3i)
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*p
  complex a0 = s*p
  z = #pixel*2
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet100_1_0"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet100_1_0"
  power = power
  bailout = bailout
}

Meet111_n_0 {
; Generic Mandelbrot set
init:
  complex u = #pixel
  complex an4 = 1/(@n + 4)
  complex an3 = 1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = 1/(@n + 1)
  complex t = (an2*an3*u - an3*an4)/(an1*an2*u - an2*an3)
  an3 = -(1 + u + t)*an3
  an2 = (u + t + u*t)*an2
  an1 = -u*t*an1
  complex un1 = u^(@n + 1)
  complex tn1 = t^(@n + 1)
  complex m = (((an4*u + an3)*u + an2)*u + an1)*un1
  complex l = (((an4*t + an3)*t + an2)*t + an1)*tn1
  if @swap1_n
    complex s = l*t/(l - m)
  else
    complex s = (l*t - m)/(l - m)
  endif
  complex p = ((t - s)/m)^(1/(@n + 3))
  an3 = an3*p
  an2 = an2*p*p
  an1 = an1*p*p*p
  complex a0 = s*p
  z = a0
loop:
  z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Meet111_n_0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param swap1_n
    caption = "Swap1_n"
    default = false
    hint = "Converts this to a Merge11n_1_0"
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet111_n_0"
  seed = #pixel
  power = power
  n = n
  swap1_n = swap1_n
  bailout = bailout
}


Jeet111_n_0 {

; Generic Julia set
init:
  complex u = @seed
  complex an4 = 1/(@n + 4)
  complex an3 = 1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = 1/(@n + 1)
  complex t = (an2*an3*u - an3*an4)/(an1*an2*u - an2*an3)
  an3 = -(1 + u + t)*an3
  an2 = (u + t + u*t)*an2
  an1 = -u*t*an1
  complex un1 = u^(@n + 1)
  complex tn1 = t^(@n + 1)
  complex m = (((an4*u + an3)*u + an2)*u + an1)*un1
  complex l = (((an4*t + an3)*t + an2)*t + an1)*tn1
  if @swap1_n
    complex s = l*t/(l - m)
  else
    complex s = (l*t - m)/(l - m)
  endif
  complex p = ((t - s)/m)^(1/(@n + 3))
  an3 = an3*p
  an2 = an2*p*p
  an1 = an1*p*p*p
  complex a0 = s*p
  z = #pixel*2
loop:
  z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet111_n_0"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param swap1_n
    caption = "Swap1_n"
    default = false
    hint = "Converts this to a Merge11n_1_0"
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet111_n_0"
  power = power
  bailout = bailout
}

Meet100_n_0 {
; Generic Mandelbrot set
init:
  complex u = #pixel
  if @insout
    u = 1/u + 1
  endif
  complex an2 = 1/(@n + 2)
  complex an1 = 1/(@n + 1)
  complex t = ((@n + 1)*u - (@n + 2))*u^(@n + 1)
  complex s = (@n + 2 + (@n + 1)*u*t)/((@n + 1)*(1 + t))
  complex p = ((@n + 1)*(@n + 2)*(s - u))^(1/(@n + 1))
  an1 = -an1*p
  complex a0 = s*p
  z = a0
loop:
  z = (an2*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Meet100_n_0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet100_n_0"
  seed = #pixel
  power = power
  n = n
  insout = insout
  bailout = bailout
}


Jeet100_n_0 {

; Generic Julia set
init:
  complex u = @seed
  if @insout
    u = 1/u + 1
  endif
  complex an2 = 1/(@n + 2)
  complex an1 = 1/(@n + 1)
  complex t = ((@n + 1)*u - (@n + 2))*u^(@n + 1)
  complex s = (@n + 2 + (@n + 1)*u*t)/((@n + 1)*(1 + t))
  complex p = ((@n + 1)*(@n + 2)*(s - u))^(1/(@n + 1))
  an1 = -an1*p
  complex a0 = s*p
  z = #pixel*2
loop:
  z = (an2*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet100_n_0"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet100_n_0"
  power = power
  bailout = bailout
}

Chebychain {
; Generic Mandelbrot set
init:
  complex s = #pixel
  complex t = 0
  complex u = 0
  int usign = 1
  if @insout
    if @geomtree == 3
      if @nd == 0
        if @lowfix
          if @fold
            s = 1/s + sqr(#pi)
          else
            s = 1/s + #pi
          endif
        else
          s = 1/s
        endif
      elseif @lowfix
        if @coslimit

          s = 1/s
        elseif 2*@nd == @n
          if @fold
            s = 1/s - 1/(4*sqr(tan(#pi/@n)))
          else
            s = 1/s - 1/(4*sqr(tan(0.5*#pi/@n)))
          endif
          s = sqrt(s) - 0.5
          s = 1/s + 1
        elseif @fold

          s = flip(1)/s - 0.5 - flip(1)/(2*tan(#pi/@n))
          s = 1/s + 1
;          s = 1/s + exp(flip(2)*#pi/@n)
        else
          s = flip(1)/s - 0.5 - flip(1)/(2*tan(0.5*#pi/@n))
          s = 1/s + 1
;          s = 1/s + exp(flip(1)*#pi/@n)
        endif
      else
        if 2*@nd == @n
          s = sqrt(s)
        endif
        s = flip(1)*s - 0.5
        s = 1/s + 1
      endif
    elseif @coslimit
      s = 1/s + 1
    elseif @fold
      s = 1/s + sqr(@n*cos((@n - 2)*#pi/(2*@n))/#pi)
    else
      s = 1/s + @n*cos((@nd + 1)*#pi/@n)/#pi
    endif
  endif
  if @fold
    if @coslimit && (@nd != 0) && (@geomtree == 3)
      s = flip(1)*s
      s = ((s + 1)/(s - 1))
      s = flip(1)*log(s)
    elseif @coslimit && (@nd != 0) && (@geomtree == 2)
      s = sqrt(1/s + 1)
      s = flip(1)*((s + 1)/(s - 1))
      s = flip(1)*log(s)/#pi
    elseif (@geomtree == 2) && (floor(0.5*@n) != 0.5*@n) && (@nd != 0)
      s = sqrt(1/s + 1)
      s = flip(1)*((s + 1)/(s - 1))
    else
      s = sqrt(s)
    endif
  endif
  if @geomtree == 3
    if @coslimit
      usign = 1
    elseif @nd == 0
      if floor(0.25*@n) == 0.25*@n
        usign = 1
      else
        usign = -1
      endif
    else
      if floor(0.5*@nd) == 0.5*@nd
        usign = 1
      else
        usign = -1
      endif
    endif
    if @lowfix
      usign = -usign
    endif
;    if @coslimit
;      s = s*#pi
;    else
;      s = s*#pi/@n
;    endif
    if (@nd != 0) && !@coslimit
      complex u = cos(@nd*#pi/@n)
      complex v = sin(@nd*#pi/@n)
      complex r = flip(0.5)*(s - 1/s)
      s = 0.5*(s + 1/s)
      complex t = s*u + r*v
      s = s*u - r*v
    elseif  (@nd != 0) && @coslimit
      t = s + 2*#pi*@nd
    else
      t = -s
    endif
  elseif @coslimit
    s = s*#pi
    complex u = 0
    int usign = 1
  elseif (@geomtree == 2) && (@nd != 0)
    complex u = cos(@nd*#pi/@n)
    complex v = sin(@nd*#pi/@n)
    complex r = flip(0.5)*(s - 1/s)
    s = 0.5*(s + 1/s)
    complex t = s*u + r*v
    s = s*u - r*v
  else
    s = s*#pi/@n
    if @fold
      complex u = 0
      if floor(0.25*@n) == 0.25*@n
        int usign = 1
      else
        int usign = -1
      endif
    else
      complex u = cos(@nd*#pi/@n)
      if floor(0.5*@nd) == 0.5*@nd
        int usign = 1
      else
        int usign = -1
      endif
    endif
  endif
  complex ss = sqr(s)
  complex sf = 0
  if @coslimit
    sf = cos(s)
  elseif @n == 3
    sf = (4*ss - 3)*s
  elseif @n == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  if @geomtree == 3
    complex p = (s - t)/(usign - sf)
    complex a0 = s - usign*p
    z = a0 - usign*p
  elseif @geomtree == 2
    if @nd == 0
      complex p = s
      if @coslimit && (floor(0.5*@n) != 0.5*@n)
        complex a0 = 0.5*#pi
        z = p + a0
      else
        complex a0 = 0
        z = p
      endif
    else
      if @coslimit
        complex p = @nd*#pi
        complex a0 = s + p
        z = s
      else
        complex p = 0.5*(s - t)
        complex a0 = 0.5*(s + t)
        z = s
      endif
    endif
  elseif @geomtree == 1
    complex p = s
    complex a0 = u + p*usign
    z = u
  else
    complex p = (u - s)/(sf + usign)
    complex a0 = u - sf*p
    z = u
  endif
  complex zf = 0
loop:
  complex zz = sqr(z)
  if @coslimit
    zf = cos(z)
  elseif @n == 3
    zf = (4*zz - 3)*z
  elseif @n == 4
    zf = ((8*zz - 8)*zz + 1)
  elseif @n == 5
    zf = ((16*zz - 20)*zz + 5)*z
  elseif @n == 6
    zf = (((32*zz - 48)*zz + 18)*zz - 1)
  elseif @n == 7
    zf = (((64*zz - 112)*zz + 56)*zz - 7)*z
  elseif @n == 8
    zf = (2*sqr(2*sqr(2*zz - 1) - 1) - 1)
  elseif @n == 9
    zf = (4*zz - 3)*z
    zf = (4*sqr(zf) - 3)*zf
  elseif @n == 16
    zf = (2*sqr(2*sqr(2*sqr(2*zz - 1) - 1) - 1) - 1)
  elseif @n == 27
    zf = (4*zz - 3)*z
    zf = (4*sqr(zf) - 3)*zf
    zf = (4*sqr(zf) - 3)*zf
  elseif @n == 32
    zf = (2*sqr(2*sqr(2*sqr(2*sqr(2*zz - 1) - 1) - 1) - 1) - 1)
  else
    zf = (2*zz - 1)
  endif
  z = zf*p + a0
bailout:
  |z| <= @bailout
default:
  title = "Chebychain"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."
  endparam
  param n
    caption = "Order"
    default = 3
    hint = "This defines the order of the Chebyshev polynomial."
  endparam
  param nd
    caption = "Destination"
    default = 0
    hint = "This defines the destination critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param coslimit
    caption = "Cosine limit"
    default = false
    hint = "As order approaches infinity we get a cosine \
            with chained critical points."
  endparam
  param fold

    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 1280000.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jhebychain"
  seed = #pixel
  power = power
  n = n
  nd = nd
  coslimit = coslimit
  geomtree = geomtree
  lowfix = lowfix
  insout = insout
  fold = fold
  bailout = bailout
}


Jhebychain {

; Generic Julia set
init:
  complex s = @seed
  complex t = 0
  complex u = 0
  int usign = 1
  if @insout
    if @geomtree == 3
      if @nd == 0
        if @lowfix
          if @fold
            s = 1/s + sqr(#pi)
          else
            s = 1/s + #pi
          endif
        else
          s = 1/s
        endif
      elseif @lowfix
        if @coslimit
          s = 1/s
        elseif 2*@nd == @n
          if @fold
            s = 1/s - 1/(4*sqr(tan(#pi/@n)))
          else
            s = 1/s - 1/(4*sqr(tan(0.5*#pi/@n)))
          endif
          s = sqrt(s) - 0.5
          s = 1/s + 1
        elseif @fold
          s = flip(1)/s - 0.5 - flip(1)/(2*tan(#pi/@n))
          s = 1/s + 1
;          s = 1/s + exp(flip(2)*#pi/@n)
        else
          s = flip(1)/s - 0.5 - flip(1)/(2*tan(0.5*#pi/@n))
          s = 1/s + 1
;          s = 1/s + exp(flip(1)*#pi/@n)
        endif
      else
        if 2*@nd == @n
          s = sqrt(s)
        endif
        s = flip(1)*s - 0.5
        s = 1/s + 1
      endif
    elseif @coslimit
      s = 1/s + 1
    elseif @fold
      s = 1/s + sqr(@n*cos((@n - 2)*#pi/(2*@n))/#pi)
    else
      s = 1/s + @n*cos((@nd + 1)*#pi/@n)/#pi
    endif
  endif
  if @fold
    if @coslimit && (@nd != 0) && (@geomtree == 3)
      s = flip(1)*s
      s = ((s + 1)/(s - 1))
      s = flip(1)*log(s)
    elseif @coslimit && (@nd != 0) && (@geomtree == 2)
      s = sqrt(1/s + 1)
      s = flip(1)*((s + 1)/(s - 1))
      s = flip(1)*log(s)/#pi
    elseif (@geomtree == 2) && (floor(0.5*@n) != 0.5*@n) && (@nd != 0)
      s = sqrt(1/s + 1)
      s = flip(1)*((s + 1)/(s - 1))
    else
      s = sqrt(s)
    endif
  endif
  if @geomtree == 3
    if @coslimit
      usign = 1
    elseif @nd == 0
      if floor(0.25*@n) == 0.25*@n
        usign = 1
      else
        usign = -1
      endif
    else
      if floor(0.5*@nd) == 0.5*@nd
        usign = 1
      else
        usign = -1
      endif
    endif
    if @lowfix
      usign = -usign
    endif
;    if @coslimit
;      s = s*#pi
;    else
;      s = s*#pi/@n
;    endif
    if (@nd != 0) && !@coslimit
      complex u = cos(@nd*#pi/@n)
      complex v = sin(@nd*#pi/@n)
      complex r = flip(0.5)*(s - 1/s)
      s = 0.5*(s + 1/s)
      complex t = s*u + r*v
      s = s*u - r*v
    elseif  (@nd != 0) && @coslimit
      t = s + 2*#pi*@nd
    else
      t = -s
    endif
  elseif @coslimit
    s = s*#pi
    complex u = 0
    int usign = 1
  elseif (@geomtree == 2) && (@nd != 0)
    complex u = cos(@nd*#pi/@n)
    complex v = sin(@nd*#pi/@n)
    complex r = flip(0.5)*(s - 1/s)
    s = 0.5*(s + 1/s)
    complex t = s*u + r*v
    s = s*u - r*v
  else
    s = s*#pi/@n
    if @fold
      complex u = 0
      if floor(0.25*@n) == 0.25*@n
        int usign = 1
      else
        int usign = -1
      endif
    else
      complex u = cos(@nd*#pi/@n)
      if floor(0.5*@nd) == 0.5*@nd
        int usign = 1
      else
        int usign = -1
      endif
    endif
  endif
  complex ss = sqr(s)
  complex sf = 0
  if @coslimit
    sf = cos(s)
  elseif @n == 3
    sf = (4*ss - 3)*s
  elseif @n == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  if @geomtree == 3
    complex p = (s - t)/(usign - sf)
    complex a0 = s - usign*p
    z = a0 - usign*p
  elseif @geomtree == 2
    if @nd == 0
      complex p = s
      if @coslimit && (floor(0.5*@n) != 0.5*@n)
        complex a0 = 0.5*#pi
        z = p + a0
      else
        complex a0 = 0
        z = p
      endif
    else
      if @coslimit
        complex p = @nd*#pi
        complex a0 = s + p
        z = s
      else
        complex p = 0.5*(s - t)
        complex a0 = 0.5*(s + t)
        z = s
      endif
    endif
  elseif @geomtree == 1
    complex p = s
    complex a0 = u + p*usign
    z = u
  else
    complex p = (u - s)/(sf + usign)
    complex a0 = u - sf*p
    z = u
  endif
  complex zf = 0
  if @coslimit
    z = #pi*#pixel
  else
    z = #pi*#pixel/@n
  endif
loop:
  complex zz = sqr(z)
  if @coslimit
    zf = cos(z)
  elseif @n == 3
    zf = (4*zz - 3)*z
  elseif @n == 4
    zf = ((8*zz - 8)*zz + 1)
  elseif @n == 5
    zf = ((16*zz - 20)*zz + 5)*z
  elseif @n == 6
    zf = (((32*zz - 48)*zz + 18)*zz - 1)
  elseif @n == 7
    zf = (((64*zz - 112)*zz + 56)*zz - 7)*z
  elseif @n == 8
    zf = (2*sqr(2*sqr(2*zz - 1) - 1) - 1)
  elseif @n == 9
    zf = (4*zz - 3)*z
    zf = (4*sqr(zf) - 3)*zf
  elseif @n == 16
    zf = (2*sqr(2*sqr(2*sqr(2*zz - 1) - 1) - 1) - 1)
  elseif @n == 27
    zf = (4*zz - 3)*z
    zf = (4*sqr(zf) - 3)*zf
    zf = (4*sqr(zf) - 3)*zf
  elseif @n == 32
    zf = (2*sqr(2*sqr(2*sqr(2*sqr(2*zz - 1) - 1) - 1) - 1) - 1)
  else

    zf = (2*zz - 1)
  endif
  z = zf*p + a0
bailout:
  |z| <= @bailout
default:
  title = "Jhebychain"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam

  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param nd
    caption = "Destination"
    default = 0
    hint = "This defines the destination critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param fold
    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0."
  endparam
  param coslimit
    caption = "Cosine limit"
    default = false
    hint = "As order approaches infinity we get a cosine \
            with chained critical points."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Chebychain"
  power = power
  bailout = bailout
}

Cube3crit {
; Generic Mandelbrot set
init:
  complex s = #pixel
  if @fold
    if @geomtree == 38 || @geomtree == 37 || @geomtree == 39 || @geomtree == 41
      s = sqrt(s)
    elseif @geomtree == 40
      s = sqrt(1/s + 1)
      s = 2*(s - 1)/(9*(s + 1))
    elseif @geomtree == 21
      s = s^(1/3)
    elseif @geomtree == 18 || @geomtree == 19 || @geomtree == 20
      s = 1/(-sqrt(1/s + 2.25) + 1.5)
    elseif @geomtree == 15
      s = sqrt(s)
      s = (1 + s)/(1 - s)
      s = s^(1/3)
      complex cr3 = 0.5*(sqrt(3) + flip(1))
      s = (cr3*s*cr3 + 1)/(sqrt(3)*(s*cr3 + cr3))
    else
      s = sqrt(s) + 0.5
    endif
  endif
  if @insout
    s = 1/s - 1
  endif
  if @nd == 0
    complex t = s - sqr(s)
    complex u = s - 1
    s = -s
  elseif @nd == 1
    complex u = s - sqr(s)
    complex t = s - 1
    s = -s
  elseif @nd == 2
    complex t = -s
    complex u = s - sqr(s)
    s = s - 1
  elseif @nd == 3
    complex u = -s
    complex t = s - sqr(s)
    s = s - 1
  elseif @nd == 4
    complex t = s - 1
    complex u = -s
    s = s - sqr(s)
  else
    complex u = s - 1
    complex t = -s
    s = s - sqr(s)
  endif
  complex a1 = -2*(s + u + t)
  complex am1 = 2*s*u*t
  complex uf = (u + a1)*u + am1/u
  complex tf = (t + a1)*t + am1/t
  if @geomtree == 42
    complex qrad = 3*(((((sqr(s) - 3)*s + 10)*s + 9)*s - 42)*s + 52)
    qrad = 3*sqrt(qrad)
    if (imag(qrad) < 0)
      qrad = -qrad
    endif
    a1 = 54*(((5*s + 3)*s - 21)*s + 40 + qrad)/(((s - 12)*s + 21)*s + 98)
    a1 = a1^(1/3)
    p = (s - 1)*2/(3*a1)
    am1 = 1
    a0 = (a1*p - 4)*a1/12
    complex ca2 = 0.5*a1
    complex ca1 = 0
    complex ca0 = -0.5
    complex cq = (3*ca1 - ca2*ca2)/9
    complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
    if real(cr) < 0
      complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
    else
      complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
    endif
    complex wi = cq/w
    complex s = w - wi - ca2/3
    s = ((s + a1)*s + am1/s)*p + a0
  elseif @geomtree == 41
    p = -s
    a0 = -3*s*s*s + 3*s
    a1 = 1/s - 3*s
    am1 = s - s*s*s
    t = 0.5*(1/s + 3*s)
    t = 0.5*(-t - sqrt(sqr(t) - 4))
    s = t + s
  elseif @geomtree == 40
;    s = s + 3
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)

    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    p = s
    a0 = u - p*uf
    s = t
  elseif @geomtree == 39
    p = s
    a0 = 3*s*s*s + s - 2*s*s/conj(s)
    a1 = 1/conj(s) - 3*s
    am1 = s*s/conj(s) - s*s*s
    t = 0.5*(1/conj(s) + 3*s)
    t = 0.5*(-t + sqrt(sqr(t) - 4*s/conj(s)))
    s = t + s
  elseif @geomtree == 38
    p = s
    a0 = 3*s*s*s + s + 2*s*s/conj(s)
    a1 = -1/conj(s) - 3*s
    am1 = -s*s/conj(s) - s*s*s
    t = 0.5*(-1/conj(s) + 3*s)
    t = 0.5*(-t + sqrt(sqr(t) + 4*s/conj(s)))
    s = t + s
  elseif @geomtree == 37
    p = s
    a0 = 3*s*s*s - s
    a1 = 1/s - 3*s
    am1 = s - s*s*s
    t = 0.5*(1/s + 3*s)
    t = 0.5*(-t + sqrt(sqr(t) - 4))
    s = t + s
  elseif @geomtree == 36
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - 2*(t + t))/(tf - sf)
    a0 = s - p*tf
    s = t
  elseif @geomtree == 35
    s = s - 1.5
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - 2*(t + t))/(uf - sf)
    a0 = s - p*uf
    s = t
  elseif @geomtree == 34
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - t)/(tf - sf)
    a0 = s - p*tf
    s = u
  elseif @geomtree == 33
    s = s + 3
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - u)/(uf - sf)
    a0 = s - p*uf
    s = t
  elseif @geomtree == 32
    s = s + 3
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)



    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - 0)/(uf - sf)
    a0 = s - p*uf
    s = t
  elseif @geomtree == 31
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - 0)/(tf - sf)
    a0 = s - p*tf
    s = u
  elseif @geomtree == 30
    s = 9/(s + 1) - 0.5
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - t)/(uf - sf)
    a0 = s - p*uf
    s = t
  elseif @geomtree == 29
    s = s
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - u)/(tf - sf)
    a0 = s - p*tf
    s = u
  elseif @geomtree == 28
    p = -s
    s = -0.5
    u = 1
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = 0 - p*uf
  elseif @geomtree == 27
    p = -s
    s = 1
    u = -0.5
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = 0 - p*uf
  elseif @geomtree == 26
    p = -s
    s = 1
    u = -0.5
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = 2*(t + s) - p*uf
  elseif @geomtree == 25
    p = -s
    s = 1
    u = -0.5
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = 2*(t + s) - p*tf
  elseif @geomtree == 24
    p = -s

    s = 1
    u = -0.5
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = s - p*uf
  elseif @geomtree == 23
    p = -s
    s = -0.5
    u = 1
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = s - p*uf
  elseif @geomtree == 22
    p = (u - 2*(s + u))/(tf - uf)
    a0 = u - tf*p
  elseif @geomtree == 21
    p = s
    a0 = 0
    a1 = 0
    am1 = 2
    s = 1
  elseif @geomtree == 20
    p = (t - 2*(t + u))/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 19
    p = (t - 2*(t + s))/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 18
    p = (t - s)/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 17
    p = (t - 0)/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 16
    p = (u - t)/(tf - uf)
    a0 = u - tf*p
  elseif @geomtree == 15
    p = (t - u)/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 14
    p = (2*(t + s) - 2*(u + s))/(tf - uf)
    a0 = 2*(t + s) - tf*p
  elseif @geomtree == 13
    p = (2*(t + s) - 0)/(tf - uf)
    a0 = 2*(t + s) - tf*p
  elseif @geomtree == 12
    p = (2*(u + s) - 0)/(tf - uf)
    a0 = 2*(u + s) - tf*p
  elseif @geomtree == 11
    p = (2*(u + t) - 0)/(tf - uf)
    a0 = 2*(u + t) - tf*p
  elseif @geomtree == 10
    p = (u - 0)/(tf - uf)
    a0 = u - tf*p
  elseif @geomtree == 9
    p = (s - 0)/(tf - uf)
    a0 = s - tf*p
  elseif @geomtree == 8
    p = (2*(u + s) - 2*(t + s))/(tf - uf)
    a0 = 2*(u + s) - tf*p
  elseif @geomtree == 7
    p = (2*(u + t) - 2*(t + s))/(tf - uf)
    a0 = 2*(u + t) - tf*p
  elseif @geomtree == 6
    p = (u - 2*(t + s))/(tf - uf)
    a0 = u - tf*p
  elseif @geomtree == 5
    p = (s - 2*(t + s))/(tf - uf)
    a0 = s - tf*p
  elseif @geomtree == 4
    p = (s - 2*(u + s))/(tf - uf)
    a0 = s - tf*p
  elseif @geomtree == 3
    p = (2*(s + t) - 2*(u + t))/(tf - uf)
    a0 = 2*(s + t) - tf*p

  elseif @geomtree == 2
    p = (s - 2*(u + t))/(tf - uf)
    a0 = s - tf*p
  elseif @geomtree == 1
    p = (u - 2*(u + t))/(tf - uf)
    a0 = u - tf*p
  else
    p = (u - s)/(tf - uf)
    a0 = u - tf*p
  endif
  complex bailval = @bailout/|p|
  complex pd = 0
  if @bailany
    pd = p*sqrt(1/3)*@windage
  endif
  zd = @bailout
  z = ((s + a1)*s + am1/s)*p + a0
loop:
  complex zi = 1/z
  if @bailany
    zd = zd*pd*(2*z + a1 - am1*sqr(zi))
  endif
  z = ((z + a1)*z + am1*zi)*p + a0
bailout:
  (|z| <= bailval) && (|zd| > 1)
default:
  title = "Cube3crit"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."

  endparam
  param n
    caption = "Order"
    default = 3
    hint = "This defines the order of the Chebyshev polynomial."
  endparam
  param nd
    caption = "Destination"
    default = 0
    hint = "This defines the destination critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = true
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param bailany
    caption = "Black Chaos"
    default = false
    hint = "Bail out on hitting any attractor."
  endparam
  param windage
    caption = "Kentucky"
    default = 1.0
    hint = "Windage for the convergance criteria."
  endparam
  param fold
    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0.5."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 1280000.0

    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jube3crit"
  seed = #pixel
  power = power
  n = n
  nd = nd
  bailany = bailany
  windage = windage
  geomtree = geomtree
  lowfix = lowfix
  insout = insout
  fold = fold
  bailout = bailout
}


Jube3crit {

; Generic Julia set
init:
  complex s = @seed
  if @fold
    if @geomtree == 38 || @geomtree == 37 || @geomtree == 39 || @geomtree == 41
      s = sqrt(s)
    elseif @geomtree == 40
      s = sqrt(1/s + 1)
      s = 2*(s - 1)/(9*(s + 1))
    elseif @geomtree == 21
      s = s^(1/3)
    elseif @geomtree == 18 || @geomtree == 19 || @geomtree == 20
      s = 1/(-sqrt(1/s + 2.25) + 1.5)
    elseif @geomtree == 15
      s = sqrt(s)
      s = (1 + s)/(1 - s)
      s = s^(1/3)
      complex cr3 = 0.5*(sqrt(3) + flip(1))
      s = (cr3*s*cr3 + 1)/(sqrt(3)*(s*cr3 + cr3))
    else
      s = sqrt(s) + 0.5
    endif
  endif
  if @insout
    s = 1/s - 1
  endif
  if @nd == 0
    complex t = s - sqr(s)
    complex u = s - 1
    s = -s
  elseif @nd == 1
    complex u = s - sqr(s)
    complex t = s - 1
    s = -s
  elseif @nd == 2
    complex t = -s
    complex u = s - sqr(s)
    s = s - 1
  elseif @nd == 3
    complex u = -s
    complex t = s - sqr(s)
    s = s - 1
  elseif @nd == 4
    complex t = s - 1
    complex u = -s
    s = s - sqr(s)
  else
    complex u = s - 1
    complex t = -s
    s = s - sqr(s)
  endif
  complex a1 = -2*(s + u + t)
  complex am1 = 2*s*u*t
  complex uf = (u + a1)*u + am1/u
  complex tf = (t + a1)*t + am1/t
  if @geomtree == 42
    complex qrad = 3*sqrt(3*(((((sqr(s) - 3)*s + 10)*s + 9)*s - 42)*s + 52))
    if (imag(qrad) < 0)
      qrad = -qrad
    endif
    a1 = 54*(((5*s + 3)*s - 21)*s + 40 + qrad)/(((s - 12)*s + 21)*s + 98)
    a1 = a1^(1/3)
    p = (s - 1)*2/(3*a1)
    am1 = 1
    a0 = (a1*p - 4)*a1/12
  elseif @geomtree == 41
    p = -s
    a0 = -3*s*s*s + 3*s
    a1 = 1/s - 3*s
    am1 = s - s*s*s
    t = 0.5*(1/s + 3*s)
    t = 0.5*(-t - sqrt(sqr(t) - 4))
    s = t + s
  elseif @geomtree == 40
;    s = s + 3
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    p = s
    a0 = u - p*uf
    s = t
  elseif @geomtree == 39
    p = s
    a0 = 3*s*s*s + s - 2*s*s/conj(s)
    a1 = 1/conj(s) - 3*s
    am1 = s*s/conj(s) - s*s*s
    t = 0.5*(1/conj(s) + 3*s)
    t = 0.5*(-t + sqrt(sqr(t) - 4*s/conj(s)))
    s = t + s
  elseif @geomtree == 38
    p = s
    a0 = 3*s*s*s + s + 2*s*s/conj(s)
    a1 = -1/conj(s) - 3*s
    am1 = -s*s/conj(s) - s*s*s
    t = 0.5*(-1/conj(s) + 3*s)
    t = 0.5*(-t + sqrt(sqr(t) + 4*s/conj(s)))
    s = t + s
  elseif @geomtree == 37
    p = s
    a0 = 3*s*s*s - s
    a1 = 1/s - 3*s
    am1 = s - s*s*s
    t = 0.5*(1/s + 3*s)
    t = 0.5*(-t + sqrt(sqr(t) - 4))
    s = t + s
  elseif @geomtree == 36
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - 2*(t + t))/(tf - sf)
    a0 = s - p*tf
    s = t
  elseif @geomtree == 35
    s = s - 1.5
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)

    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - 2*(t + t))/(uf - sf)
    a0 = s - p*uf
    s = t
  elseif @geomtree == 34
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - t)/(tf - sf)
    a0 = s - p*tf
    s = u
  elseif @geomtree == 33
    s = s + 3
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - u)/(uf - sf)
    a0 = s - p*uf
    s = t
  elseif @geomtree == 32
    s = s + 3
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - 0)/(uf - sf)
    a0 = s - p*uf
    s = t
  elseif @geomtree == 31
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - 0)/(tf - sf)
    a0 = s - p*tf
    s = t
  elseif @geomtree == 30
    s = 9/(s + 1) - 0.5
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - t)/(uf - sf)
    a0 = s - p*uf
    s = t
  elseif @geomtree == 29
    s = s
    u = -0.5
    t = 1
    complex a1 = -2*(t + u + t)
    complex am1 = 2*t*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    complex sf = (s + a1)*s + am1/s
    p = (s - u)/(tf - sf)
    a0 = s - p*tf
    s = u
  elseif @geomtree == 28
    p = -s
    s = -0.5
    u = 1
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = 0 - p*uf
  elseif @geomtree == 27
    p = -s
    s = 1
    u = -0.5
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = 0 - p*uf
  elseif @geomtree == 26
    p = -s
    s = 1
    u = -0.5
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = 2*(t + s) - p*uf
  elseif @geomtree == 25
    p = -s
    s = 1
    u = -0.5
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = 2*(t + s) - p*tf
  elseif @geomtree == 24
    p = -s
    s = 1
    u = -0.5
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = s - p*uf
  elseif @geomtree == 23
    p = -s
    s = -0.5
    u = 1
    t = 1
    complex a1 = -2*(s + u + t)
    complex am1 = 2*s*u*t
    complex uf = (u + a1)*u + am1/u
    complex tf = (t + a1)*t + am1/t
    a0 = s - p*uf
  elseif @geomtree == 22
    p = (u - 2*(s + u))/(tf - uf)
    a0 = u - tf*p
  elseif @geomtree == 21
    p = s
    a0 = 0
    a1 = 0
    am1 = 2
    s = 1
  elseif @geomtree == 20
    p = (t - 2*(t + u))/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 19
    p = (t - 2*(t + s))/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 18
    p = (t - s)/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 17
    p = (t - 0)/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 16
    p = (u - t)/(tf - uf)
    a0 = u - tf*p
  elseif @geomtree == 15
    p = (t - u)/(tf - uf)
    a0 = t - tf*p
  elseif @geomtree == 14

    p = (2*(t + s) - 2*(u + s))/(tf - uf)


    a0 = 2*(t + s) - tf*p
  elseif @geomtree == 13
    p = (2*(t + s) - 0)/(tf - uf)
    a0 = 2*(t + s) - tf*p
  elseif @geomtree == 12
    p = (2*(u + s) - 0)/(tf - uf)
    a0 = 2*(u + s) - tf*p
  elseif @geomtree == 11
    p = (2*(u + t) - 0)/(tf - uf)
    a0 = 2*(u + t) - tf*p
  elseif @geomtree == 10
    p = (u - 0)/(tf - uf)
    a0 = u - tf*p
  elseif @geomtree == 9
    p = (s - 0)/(tf - uf)
    a0 = s - tf*p
  elseif @geomtree == 8
    p = (2*(u + s) - 2*(t + s))/(tf - uf)
    a0 = 2*(u + s) - tf*p
  elseif @geomtree == 7
    p = (2*(u + t) - 2*(t + s))/(tf - uf)
    a0 = 2*(u + t) - tf*p
  elseif @geomtree == 6
    p = (u - 2*(t + s))/(tf - uf)
    a0 = u - tf*p

  elseif @geomtree == 5
    p = (s - 2*(t + s))/(tf - uf)
    a0 = s - tf*p
  elseif @geomtree == 4
    p = (s - 2*(u + s))/(tf - uf)
    a0 = s - tf*p
  elseif @geomtree == 3
    p = (2*(s + t) - 2*(u + t))/(tf - uf)
    a0 = 2*(s + t) - tf*p
  elseif @geomtree == 2
    p = (s - 2*(u + t))/(tf - uf)
    a0 = s - tf*p
  elseif @geomtree == 1
    p = (u - 2*(u + t))/(tf - uf)
    a0 = u - tf*p
  else
    p = (u - s)/(tf - uf)
    a0 = u - tf*p
  endif
  complex bailval = @bailout/|p|
  z = #pixel/p
  complex pd = 0
  if @bailany
    pd = p*sqrt(1/3)*@windage
  endif
  zd = @bailout
loop:
  complex zi = 1/z
  if @bailany
    zd = zd*pd*(2*z + a1 - am1*sqr(zi))
  endif
  z = ((z + a1)*z + am1*zi)*p + a0
bailout:
  (|z| <= bailval) && (|zd| > 1)
default:
  title = "Jube3crit"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param nd
    caption = "Destination"
    default = 0
    hint = "This defines the destination critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = true
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param fold
    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0."
  endparam
  param windage
    caption = "Kentucky"
    default = 1.0
    hint = "Windage for the convergance criteria."
  endparam

  param bailany
    caption = "Black Chaos"
    default = false
    hint = "Bail out on hitting any attractor."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Cube3crit"
  power = power
  bailout = bailout
}

Cube4crit {
; Generic Mandelbrot set
init:
  complex s = #pixel
  if @fold
    if @geomtree == 35
      s = sqrt(1/s + 1)
      s = 3*(s - 1)/(s + 1)
    elseif @geomtree == 30
      s = sqrt(1/(sqrt(1/s + 1.25) + 0.5) - 1)
    elseif @geomtree == 29 || @geomtree == 33
      s = sqrt(1/(sqrt(s) + 0.5) - 1)
    elseif @geomtree == 21
      s = s^(1/3)
    elseif @geomtree == 19 || @geomtree == 32
      s = sqrt(9/s + 9)
      s = -(s + 1)/(s + 3)
    elseif @geomtree == 3
      s = sqrt(s)
      s = flip(2)/(s + flip(1)) - 1
      s = s^(1/3)
      complex cr3 = -0.5*(sqrt(3) + flip(1))
      s = (cr3*s*flip(1) + 1)/(sqrt(3)*(s*flip(1) + cr3))
    elseif @geomtree == 0 || @geomtree == 1
      s = flip(2)/(s + flip(1)) - 1
      s = s^(1/3)
      complex cr3 = -0.5*(sqrt(3) + flip(1))

      s = (cr3*s*flip(1) + 1)/(sqrt(3)*(s*flip(1) + cr3))
    else
      s = sqrt(s) - 0.5
    endif
  endif
  if @insout
    s = 1/s - 1/3
  endif
  complex a = s
  complex b = -(2 + 3*a)/(1 + 2*a)
  complex c = 0
  s = a*b
  if @geomtree == 46
    a = 1/a + 1
    c = 0
    p = -a/(1/3 + (a - 1/3)/(sqr(a)*(a - 3)))
    a0 = a + p/3
    a = -1/3
    b = -3
    s = a0
  elseif @geomtree == 45
    a = 1/a + 1
    c = 0
    a0 = a
    p = (1 - a)*sqr(a)*(a - 3)/(a - 1/3)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 44
    a = 1/a + 1
    c = 3*a
    a0 = a
    p = (1/a - a)*c
    a = -1/3
    b = -3
    s = 0
  elseif @geomtree == 43
    a = 1/a
    c = 0
    a0 = 1
    p = a
    a = -1/3

    b = -3
    s = 1
  elseif @geomtree == 42
    c = -sqr(a)*(a - 3)/(a - 1/3)

    a0 = 1
    p = (a - 1)*(2*c/3 - 2)*1.5
    a = -1/3
    b = -3
    s = 0
  elseif @geomtree == 41
    a = 1/a + 1
    c = -sqr(a)*(a - 3)/(a - 1/3)
    a0 = a
    p = -a0*(2*c/3 - 2)*1.5
    a = -1/3
    b = -3
    s = 0
  elseif @geomtree == 40
    a = 1/a + 1
    c = -sqr(a)*(a - 3)/(a - 1/3)
    a0 = a
    p = c*(1 - a0)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 39
    c = -sqr(a)*(a - 3)/(a - 1/3)
    a0 = 3
    p = c*(a - a0)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 38
    c = 0
    a0 = 3
    p = a
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 37
    c = 0
    a0 = a
    p = -sqr(a)*sqr(a - 3)/(a - 1/3)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 36
    c = 0
    a0 = a
    p = -a*sqr(a)*(a - 3)/(a - 1/3)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 35
    c = 0
    p = a
    a0 = 0
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 34
    a = 1/a
    a0 = real(a)
    b = 0.5*(1/a0 - a0) + 0.5*flip(imag(a))
    a = -1/conj(b)
    c = conj(a0*b)
    p = -conj(b)*(1 + sqr(a0))
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 33
    a0 = a
    b = -(1 - sqr(sqr(a0)))/(a0*(1 - sqr(a0)))
    a = 1/b
    c = -a0*b
    p = b*(sqr(a0) - 1)
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 32
    c = 0
    p = -b*s
    a0 = 0
  elseif @geomtree == 31
    a = 1/a
    a0 = real(a)
    b = -0.5*(1/a0 + a0) + flip(imag(a))
    a = 1/conj(b)
    c = conj(a0*b)
    p = conj(b)*(1 - sqr(a0))
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 30
    a0 = a
    b = -(1 + sqr(sqr(a0)))/(a0*(1 + sqr(a0)))
    a = 1/b
    c = a0*b
    p = b*(1 - sqr(a0))
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 29
    a0 = a
    b = -0.5*(1/a0 + a0)
    a = 1/b
    c = a0*b
    p = b*(1 - sqr(a0))
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 28
    complex di = -b
    complex ds = -a
    complex d0 = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 27
    complex di = s
    complex d0 = -a
    complex ds = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 26
    complex di = 1
    complex ds = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 25
    complex di = s
    complex ds = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 24
    complex di = 0
    complex ds = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 23
    complex di = -b
    complex d0 = 1
    complex ds = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 22
    complex di = s
    complex d0 = 1
    complex ds = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 21
    complex di = s
    complex d1 = -a
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 20
    a = 1/a
    c = 0
    a0 = 0
    b = a
    a = -1/conj(b)
    p = b
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 19
    c = 0
    p = b*s
    a0 = 0
  elseif @geomtree == 18
    complex di = 0
    complex d1 = s
    complex d0 = -a
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 17
    complex di = 1
    complex d1 = 0
    complex d0 = -a
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di

  elseif @geomtree == 16
    complex di = 1

    complex d1 = -b
    complex d0 = -a
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 15
    complex di = 1
    complex d1 = 0
    complex d0 = -a/(1 + 2*a)
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 14
    complex di = 0
    complex d1 = -b
    complex d0 = -a
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 13
    complex di = -b
    complex d1 = 0
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 12
    complex di = -a/(1 + 2*a)
    complex ds = -a
    complex d0 = -b
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 11
    c = 0
    a0 = s
    p = (a0 + a)/(1 + 2*a)
  elseif @geomtree == 10
    c = 0
    a0 = 1
    p = (a0*(1 + 2*a) + a)*s*sqr(b)
  elseif @geomtree == 9
    c = 0
    a0 = s
    p = (a0*(1 + 2*a) + a)*s*sqr(b)
  elseif @geomtree == 8
    complex di = -b
    complex d1 = s
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 7
    complex di = s
    complex d1 = 0
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 6
    complex di = s
    complex d1 = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 5
    complex di = -a
    complex d1 = 0
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 4
    complex di = -a
    complex d1 = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 3
    complex di = -a
    complex d0 = -b
    complex d1 = -a/(1 + 2*a)
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 2
    c = 0

    p = s/(1 + 2*a)
    a0 = s
  elseif @geomtree == 1
    c = 0
    p = 1/(1 + 2*a)
    a0 = 1
  else
    c = sqr(1 + a)/(sqr(a)*(1 + 2*a))
    p = -2*c
    a0 = -b
  endif
  complex bailval = @bailout/|p|
  complex pd = 0
  if @bailany
    pd = -2*p*sqrt(1/3)*@windage
  endif

  zd = @bailout
  complex zi = 1/((s + b)*sqr(s) + c*(s + a))
  z = (s + a)*zi*p + a0
loop:
  zi = 1/((z + b)*sqr(z) + c*(z + a))
  if @bailany
    zd = zd*pd*sqr(zi)*z*((z + 0.5*(b + 3*a))*z + a*b)
  endif
  z = (z + a)*zi*p + a0
bailout:
  (|z| <= bailval) && (|zd| > 1)
default:
  title = "Cube4crit"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0

    hint = "This defines the connection geometry of the critical points."
  endparam
  param n
    caption = "Order"
    default = 3
    hint = "This defines the order of the Chebyshev polynomial."
  endparam
  param nd
    caption = "Destination"
    default = 0
    hint = "This defines the destination critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param bailany
    caption = "Black Chaos"
    default = true
    hint = "Bail out on hitting any attractor."
  endparam
  param windage
    caption = "Kentucky"
    default = 1.0
    hint = "Windage for the convergance criteria."
  endparam
  param fold
    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0.5."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 1.28e26
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jube4crit"
  seed = #pixel
  power = power
  n = n
  nd = nd
  bailany = bailany
  windage = windage
  geomtree = geomtree
  lowfix = lowfix
  insout = insout
  fold = fold
  bailout = bailout
}


Jube4crit {

; Generic Julia set
init:
  complex s = @seed
  if @fold
    if @geomtree == 35
      s = sqrt(1/s + 1)
      s = 3*(s - 1)/(s + 1)
    elseif @geomtree == 30
      s = sqrt(1/(sqrt(1/s + 1.25) + 0.5) - 1)
    elseif @geomtree == 29 || @geomtree == 33
      s = sqrt(1/(sqrt(s) + 0.5) - 1)
    elseif @geomtree == 21
      s = s^(1/3)
    elseif @geomtree == 19 || @geomtree == 32
      s = sqrt(9/s + 9)
      s = -(s + 1)/(s + 3)
    elseif @geomtree == 3
      s = sqrt(s)
      s = flip(2)/(s + flip(1)) - 1
      s = s^(1/3)
      complex cr3 = -0.5*(sqrt(3) + flip(1))
      s = (cr3*s*flip(1) + 1)/(sqrt(3)*(s*flip(1) + cr3))
    elseif @geomtree == 0 || @geomtree == 1
      s = flip(2)/(s + flip(1)) - 1
      s = s^(1/3)
      complex cr3 = -0.5*(sqrt(3) + flip(1))
      s = (cr3*s*flip(1) + 1)/(sqrt(3)*(s*flip(1) + cr3))
    else
      s = sqrt(s) - 0.5
    endif
  endif
  if @insout
    s = 1/s - 1/3
  endif
  complex a = s
  complex b = -(2 + 3*a)/(1 + 2*a)
  complex c = 0
  s = a*b
  if @geomtree == 46
    a = 1/a + 1
    c = 0
    p = -a/(1/3 + (a - 1/3)/(sqr(a)*(a - 3)))
    a0 = a + p/3
    a = -1/3
    b = -3
    s = a0
  elseif @geomtree == 45
    a = 1/a + 1
    c = 0
    a0 = a
    p = (1 - a)*sqr(a)*(a - 3)/(a - 1/3)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 44
    a = 1/a + 1
    c = 3*a
    a0 = a
    p = (1/a - a)*c
    a = -1/3
    b = -3
    s = 0
  elseif @geomtree == 43
    a = 1/a
    c = 0
    a0 = 1
    p = a
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 42
    c = -sqr(a)*(a - 3)/(a - 1/3)
    a0 = 1
    p = (a - 1)*(2*c/3 - 2)*1.5
    a = -1/3
    b = -3
    s = 0
  elseif @geomtree == 41
    a = 1/a + 1
    c = -sqr(a)*(a - 3)/(a - 1/3)
    a0 = a
    p = -a0*(2*c/3 - 2)*1.5
    a = -1/3
    b = -3
    s = 0
  elseif @geomtree == 40
    a = 1/a + 1

    c = -sqr(a)*(a - 3)/(a - 1/3)
    a0 = a
    p = c*(1 - a0)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 39
    c = -sqr(a)*(a - 3)/(a - 1/3)
    a0 = 3
    p = c*(a - a0)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 38
    c = 0
    a0 = 3
    p = a
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 37
    c = 0
    a0 = a
    p = -sqr(a)*sqr(a - 3)/(a - 1/3)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 36
    c = 0
    a0 = a
    p = -a*sqr(a)*(a - 3)/(a - 1/3)
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 35
    c = 0
    p = a
    a0 = 0
    a = -1/3
    b = -3
    s = 1
  elseif @geomtree == 34
    a = 1/a
    a0 = real(a)
    b = 0.5*(1/a0 - a0) + 0.5*flip(imag(a))
    a = -1/conj(b)
    c = conj(a0*b)
    p = -conj(b)*(1 + sqr(a0))
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 33
    a0 = a
    b = -(1 - sqr(sqr(a0)))/(a0*(1 - sqr(a0)))
    a = 1/b
    c = -a0*b
    p = b*(sqr(a0) - 1)
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 32
    c = 0
    p = -b*s
    a0 = 0
  elseif @geomtree == 31
    a = 1/a
    a0 = real(a)
    b = -0.5*(1/a0 + a0) + flip(imag(a))
    a = 1/conj(b)
    c = conj(a0*b)
    p = conj(b)*(1 - sqr(a0))
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 30
    a0 = a
    b = -(1 + sqr(sqr(a0)))/(a0*(1 + sqr(a0)))
    a = 1/b
    c = a0*b
    p = b*(1 - sqr(a0))
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 29
    a0 = a
    b = -0.5*(1/a0 + a0)
    a = 1/b
    c = a0*b
    p = b*(1 - sqr(a0))
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 28
    complex di = -b
    complex ds = -a
    complex d0 = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 27
    complex di = s
    complex d0 = -a
    complex ds = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 26
    complex di = 1
    complex ds = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 25
    complex di = s
    complex ds = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 24
    complex di = 0
    complex ds = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 23
    complex di = -b
    complex d0 = 1
    complex ds = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 22
    complex di = s
    complex d0 = 1
    complex ds = -a/(1 + 2*a)
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 21
    complex di = s
    complex d1 = -a
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 20
    a = 1/a
    c = 0
    a0 = 0
    b = a
    a = -1/conj(b)
    p = b
    s = 0.25*(-(b + 3*a) + sqrt(sqr(b + 3*a) - 16*a*b))
  elseif @geomtree == 19
    c = 0
    p = b*s
    a0 = 0
  elseif @geomtree == 18
    complex di = 0
    complex d1 = s
    complex d0 = -a
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 17
    complex di = 1
    complex d1 = 0
    complex d0 = -a
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 16
    complex di = 1

    complex d1 = -b
    complex d0 = -a
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 15
    complex di = 1
    complex d1 = 0
    complex d0 = -a/(1 + 2*a)
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 14
    complex di = 0

    complex d1 = -b
    complex d0 = -a
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 13
    complex di = -b
    complex d1 = 0
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 12
    complex di = -a/(1 + 2*a)
    complex ds = -a
    complex d0 = -b
    c = (di - ds)*(1 + 2*a)*s*sqr(b)/(d0 - ds)
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 11
    c = 0
    a0 = s
    p = (a0 + a)/(1 + 2*a)

  elseif @geomtree == 10
    c = 0
    a0 = 1
    p = (a0*(1 + 2*a) + a)*s*sqr(b)
  elseif @geomtree == 9
    c = 0
    a0 = s
    p = (a0*(1 + 2*a) + a)*s*sqr(b)
  elseif @geomtree == 8
    complex di = -b
    complex d1 = s
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 7
    complex di = s
    complex d1 = 0
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 6
    complex di = s
    complex d1 = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 5
    complex di = -a
    complex d1 = 0
    complex d0 = 1
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 4
    complex di = -a
    complex d1 = -b
    complex d0 = -a/(1 + 2*a)
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di
  elseif @geomtree == 3
    complex di = -a
    complex d0 = -b
    complex d1 = -a/(1 + 2*a)
    c = (di - d1)/((1 + 2*a)*(d0 - d1))
    p = c*(d0 - di)
    a0 = di

  elseif @geomtree == 2
    c = 0
    p = s/(1 + 2*a)
    a0 = s
  elseif @geomtree == 1
    c = 0
    p = 1/(1 + 2*a)
    a0 = 1
  else
    c = sqr(1 + a)/(sqr(a)*(1 + 2*a))
    p = -2*c
    a0 = -b
  endif
  complex bailval = @bailout/|p|
  complex pd = 0
  if @bailany
    pd = -2*p*sqrt(1/3)*@windage


  endif

  zd = @bailout
  z = #pixel
  if @geomtree == 0 || @geomtree == 3 || @geomtree == 4
    z = 0.25/z + s
  endif
loop:
  zi = 1/((z + b)*sqr(z) + c*(z + a))
  if @bailany
    zd = zd*pd*sqr(zi)*z*((z + 0.5*(b + 3*a))*z + a*b)
  endif
  z = (z + a)*zi*p + a0
bailout:
  (|z| <= bailval) && (|zd| > 1)
default:
  title = "Jube4crit"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param nd
    caption = "Destination"
    default = 0
    hint = "This defines the destination critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = true
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix

    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param fold
    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0."
  endparam
  param windage
    caption = "Kentucky"
    default = 1.0
    hint = "Windage for the convergance criteria."
  endparam
  param bailany
    caption = "Black Chaos"
    default = false
    hint = "Bail out on hitting any attractor."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Cube4crit"
  power = power

  bailout = bailout
}

Quad2crit {
; Generic Mandelbrot set
init:
  complex s = #pixel
  complex a0 = 0
  complex a1 = 1
  if @geomtree == 23
    complex u = s
    if @uhp
      u = (u - flip(1))/(u + flip(1))
    endif
    float hr = real(@hypcent)
    float hi = imag(@hypcent)
    u = ((hr + 1)*u + (hr - 1))/((hr - 1)*u + (hr + 1))
    u = ((hi + 1)*u + flip(hi - 1))/(-flip(hi - 1)*u + (hi + 1))
    if |u| > 1
      u = 1/u
    endif
    complex fu00 = (1.83006188130296, 0)
    complex fu01 = (1.53268603745129, 0)
    complex fu02 = (1.53268603745129, 0)
    complex fu03 = (1.83006188130296, 0)
    complex fu10 = (4.97479722366339, 0)
    complex fu11 = (3.49069798919486, 3.40053451163194)
    complex fu12 = (3.49069798919486, -3.40053451163194)
    complex fu13 = (4.97479722366339, 0)
    complex fu20 = (1.60062320016132, 0)
    complex fu21 = (0, 1.24979783520963)
    complex fu22 = (0, -1.24979783520963)
    complex fu23 = (1.60062320016132, 0)
    complex fu30 = (4.97479722366339, 0)
    complex fu31 = (-3.49069798919486, 3.40053451163194)
    complex fu32 = (-3.49069798919486, -3.40053451163194)
    complex fu33 = (4.97479722366339, 0)
    complex fu40 = (1.83006188130296, 0)
    complex fu41 = (-1.53268603745129, 0)
    complex fu42 = (-1.53268603745129, 0)
    complex fu43 = (1.83006188130296, 0)
    complex fu50 = (4.97479722366339, 0)
    complex fu51 = (-3.49069798919486, -3.40053451163194)
    complex fu52 = (-3.49069798919486, 3.40053451163194)
    complex fu53 = (4.97479722366339, 0)
    complex fu60 = (1.60062320016132, 0)
    complex fu61 = (0, -1.24979783520963)
    complex fu62 = (0, 1.24979783520963)
    complex fu63 = (1.60062320016132, 0)
    complex fu70 = (4.97479722366339, 0)
    complex fu71 = (3.49069798919486, -3.40053451163194)
    complex fu72 = (3.49069798919486, 3.40053451163194)
    complex fu73 = (4.97479722366339, 0)
    complex vu00 = (-6.80319462258186, 0)
    complex vu01 = (-6.729298408655, 0)
    complex vu02 = (-6.729298408655, 0)
    complex vu03 = (-6.80319462258186, 0)
    complex vu10 = (-1.7689197870267, 0)
    complex vu11 = (-1.23660891469389, 0.774516368474021)
    complex vu12 = (-1.23660891469389, -0.774516368474021)
    complex vu13 = (-1.7689197870267, 0)
    complex vu20 = (-3.6669160814782, 0)
    complex vu21 = (0, 3.52792765637327)
    complex vu22 = (0, -3.52792765637327)
    complex vu23 = (-3.6669160814782, 0)
    complex vu30 = (-1.7689197870267, 0)
    complex vu31 = (1.2366089146939, 0.774516368474026)
    complex vu32 = (1.2366089146939, -0.774516368474026)
    complex vu33 = (-1.7689197870267, 0)
    complex vu40 = (-6.80319462258187, 0)
    complex vu41 = (6.72929840865501, 0)
    complex vu42 = (6.72929840865501, 0)
    complex vu43 = (-6.80319462258187, 0)
    complex vu50 = (-1.7689197870267, 0)
    complex vu51 = (1.23660891469389, -0.774516368474024)
    complex vu52 = (1.23660891469389, 0.774516368474024)
    complex vu53 = (-1.7689197870267, 0)
    complex vu60 = (-3.6669160814782, 0)
    complex vu61 = (0, -3.52792765637328)
    complex vu62 = (0, 3.52792765637328)
    complex vu63 = (-3.6669160814782, 0)
    complex vu70 = (-1.7689197870267, 0)
    complex vu71 = (-1.2366089146939, -0.77451636847402)
    complex vu72 = (-1.2366089146939, 0.77451636847402)
    complex vu73 = (-1.7689197870267, 0)
    complex umata = (1.81711731221675, 0.743926303451645)
    complex umatb = (-0.984102273962777, -1.37363910315131)
    complex umatc = (-0.984102273962777, 1.37363910315131)
    complex umatd = (1.81711731221675, -0.743926303451645)
    complex ffun = (0.775238238163461, 0.66715237172243)
    float ffnm = 0.0460866130
    complex vfun = (0.915597613665918, 0.822040232602688)
    float vfnm = 0.5140691341
    bool better = true
    complex t = 0
    while better
      better = false
      t = (fu00*u + fu01)/(fu02*u + fu03)
      if |t| < |u|
        better = true
        u = t
      endif
      t = (fu10*u + fu11)/(fu12*u + fu13)
      if |u + ffun| < ffnm
        better = true
        u = t
      endif
      t = (fu20*u + fu21)/(fu22*u + fu23)
      if |t| < |u|
        better = true
        u = t
      endif
      t = (fu30*u + fu31)/(fu32*u + fu33)
      if |u - conj(ffun)| < ffnm
        better = true
        u = t
      endif
      t = (fu40*u + fu41)/(fu42*u + fu43)
      if |t| < |u|
        better = true
        u = t
      endif
      t = (fu50*u + fu51)/(fu52*u + fu53)
      if |u - ffun| < ffnm
        better = true
        u = t
      endif
      t = (fu60*u + fu61)/(fu62*u + fu63)
      if |t| < |u|
        better = true
        u = t
      endif
      t = (fu70*u + fu71)/(fu72*u + fu73)
      if |u + conj(ffun)| < ffnm
        better = true
        u = t
      endif
    endwhile
    complex v = (umata*u + umatb)/(umatc*u + umatd)
    better = true
    while better
      better = false
      t = (vu00*v + vu01)/(vu02*v + vu03)
      if |t| < |v|
        better = true
        v = t
      endif
      t = (vu10*v + vu11)/(vu12*v + vu13)
      if |v + conj(vfun)| < vfnm
        better = true
        v = t
      endif
      t = (vu20*v + vu21)/(vu22*v + vu23)
      if |t| < |v|
        better = true
        v = t
      endif
      t = (vu30*v + vu31)/(vu32*v + vu33)
      if |v - vfun| < vfnm
        better = true
        v = t
      endif
      t = (vu40*v + vu41)/(vu42*v + vu43)
      if |t| < |v|
        better = true
        v = t
      endif
      t = (vu50*v + vu51)/(vu52*v + vu53)
      if |v - conj(vfun)| < vfnm
        better = true
        v = t
      endif
      t = (vu60*v + vu61)/(vu62*v + vu63)
      if |t| < |v|
        better = true
        v = t
      endif
      t = (vu70*v + vu71)/(vu72*v + vu73)
      if |v + vfun| < vfnm
        better = true
        v = t
      endif
    endwhile
    if |v| > |u|
      complex uu = u*u
      complex sz = \
        ((((((((((((((((((((((((((((((50.8285043301517*uu + \
         21.1822729720076)*uu + \
         16.765948907338)*uu + \
         43.7961380207474)*uu + \
         1.50138455967125)*uu + \
         27.1782031497161)*uu + \
         -7.44269317223692)*uu + \
         -0.226471541200099)*uu + \
         3.63505365756027)*uu + \
         -20.2540399540202)*uu + \
         -0.954747741789354)*uu + \
         -20.8675379240415)*uu + \
         1.99779330425055)*uu + \
         -12.1941098477131)*uu + \
         -3.14790838392742)*uu + \
         1.49016780408159)*uu + \
         -2.15269122870894)*uu + \
         5.29090496756078)*uu + \
         -0.544075835468025)*uu + \
         4.7195308772554)*uu + \
         4.53089725317355)*uu + \
         1.96072189949404)*uu + \
         3.84622774686998)*uu + \
         -1.12491301047044)*uu + \
         3.1611075885776)*uu + \
         -1.48090275608658)*uu + \
         0.265955064052117)*uu + \
         -0.914809768957607)*uu + \
         -0.80558574702971)*uu + \
         -0.43271738253076)*uu + \
         -0.948850047211325)*uu + \
         -0.266318358487369
      complex nz = \
        ((((3.34932481372634*uu + \
         -2.29108516679601)*uu + \
         -3.56428044938751)*uu + \
         3.17921539381276)*uu + \
         0.429033840461224)*uu + \
         1
      complex dz = \
        ((((5.4682410869534*uu + \
         -1.00326433962286)*uu + \
         -4.63083659896653)*uu + \
         0.429033840461224)*uu + \
         1)*uu
      complex sw = \
        (((((((((((((((((((((((((((((((1244.55156098388*uu + \
         -1044.85318148304)*uu + \
         1365.11006115432)*uu + \
         734.195716441453)*uu + \
         710.618884533585)*uu + \
         1358.98468918307)*uu + \
         15.7112863617801)*uu + \
         1060.64875311286)*uu + \
         -123.815283338864)*uu + \
         326.295201175061)*uu + \
         -111.590370800305)*uu + \
         -204.712545025044)*uu + \
         -25.2704061171468)*uu + \
         -328.32887144145)*uu + \
         -76.399453271931)*uu + \
         -196.33361527777)*uu + \
         -81.7934486435375)*uu + \
         -31.843023775531)*uu + \
         -77.2679391900259)*uu + \
         57.5337428147105)*uu + \
         -26.495947466048)*uu + \
         57.9291962404693)*uu + \
         7.28566661633742)*uu + \
         28.7609465707033)*uu + \
         22.536642650597)*uu + \
         8.788506347703)*uu + \
         12.0922840394811)*uu + \
         -0.831988373488552)*uu + \
         1.52752556995338)*uu + \
         -1.18976521806274)*uu + \
         -4.12466463652027)*uu + \
         -0.547056822581384)*u
      complex nw = \
        (((((((((((229.924588338754*uu + \
         -88.0861356394314)*uu + \
         -397.88217487117)*uu + \
         109.673495603488)*uu + \
         246.508977532891)*uu + \
         -38.4869271353045)*uu + \
         -40.9069618845349)*uu + \
         -1.05742260136996)*uu + \
         -5.387448424406)*uu + \
         8.74182600327833)*uu + \
         -14.6048749660359)*uu + \
         0.406788704973983)*uu + \
         1
      complex dw = \
        ((((((((((-69.9228520720704*uu + \
         32.0720606924251)*uu + \
         143.624005894562)*uu + \
         -54.3211135343213)*uu + \
         -120.346543338335)*uu + \
         34.7296841165408)*uu + \
         51.4647412805411)*uu + \
         -9.93392805301499)*uu + \
         -11.2319601794271)*uu + \
         1.07258460115308)*uu + \
         1)*uu*uu*u
    else
      complex vv = v*v
      complex sz = \
        ((((((((((((((((((((((((((((((-329.896829137034*vv + \
         535.632662850714)*vv + \
         -288.859170603267)*vv + \
         -136.186896677415)*vv + \
         283.761403759031)*vv + \
         -217.930463962149)*vv + \
         -23.5363445826578)*vv + \
         171.955234482815)*vv + \
         -124.314467349942)*vv + \
         25.6165980308276)*vv + \
         85.6870647250078)*vv + \
         -88.060327555702)*vv + \
         26.8279872568985)*vv + \
         26.7712280038119)*vv + \
         -58.9580364407965)*vv + \
         18.0525146698689)*vv + \
         13.7677240678965)*vv + \
         -26.0102371357958)*vv + \
         19.4593783521772)*vv + \
         7.19940203377203)*vv + \
         -13.4112462232443)*vv + \
         14.0437317095019)*vv + \
         -0.927034606640644)*vv + \
         -8.0940195654052)*vv + \
         4.36962946466608)*vv + \
         -2.00770760225374)*vv + \
         -3.26524229220525)*vv + \
         3.114507368033)*vv + \
         -0.477293557447735)*vv + \
         -0.634207615660206)*vv + \
         2.02989764260562)*vv + \
         0.730031515734547
      complex nz = \
        (((((((-4.99606287451219*vv + \
         2.81979769244912)*vv + \
         9.37398018603044)*vv + \
         -4.90048917295332)*vv + \
         -9.8354733320135)*vv + \
         7.18033780423563)*vv + \
         4.47509521442272)*vv + \
         -4.33082353513855)*vv
      complex dz = \
        (((((((6.94353421608628*vv + \
         -4.11293465385055)*vv + \
         -11.9219954315396)*vv + \
         4.08930170614781)*vv + \
         10.8119014669575)*vv + \
         -1.90191994136891)*vv + \
         -4.75037059355414)*vv + \
         0.143441339218172)*vv + \
         1
      complex sw = \
        (((((((((((((((((((((((((((((((-93431.4994472434*vv + \
         58158.071042987)*vv + \
         8798.90521834021)*vv + \
         -41533.5615653787)*vv + \
         32872.5932348587)*vv + \
         -3114.45150978675)*vv + \
         -17679.9057595404)*vv + \
         16558.9464899814)*vv + \
         -4762.53420355266)*vv + \
         -6531.3413236715)*vv + \
         8166.50724876673)*vv + \
         -3113.82729701504)*vv + \
         -1797.28687520996)*vv + \
         3756.97369928781)*vv + \
         -1903.94716932743)*vv + \
         -372.84232513744)*vv + \
         1407.02718322058)*vv + \
         -1055.56571478838)*vv + \
         -29.2877696137142)*vv + \
         485.543604170474)*vv + \
         -441.109754141229)*vv + \
         92.5527983672403)*vv + \
         178.668067972833)*vv + \
         -161.840442962114)*vv + \
         70.0359016559377)*vv + \
         38.5132396817261)*vv + \
         -55.6468209924833)*vv + \
         17.4224965414547)*vv + \
         2.07279297810727)*vv + \
         -16.5157882429291)*vv + \
         6.21879960338274)*vv + \
         1.19457099958621)*v
      complex nw = \
        (((((((((((((((((((-262.016818978863*vv + \
         799.2917646746)*vv + \
         342.79241953858)*vv + \
         -2709.02794743515)*vv + \
         -75.7903919274321)*vv + \
         5154.96845769143)*vv + \
         -341.050352953843)*vv + \
         -6587.67925347603)*vv + \
         452.832004767186)*vv + \
         6127.3192751211)*vv + \
         -384.03255866431)*vv + \
         -4143.63025839381)*vv + \
         301.635914862471)*vv + \
         1972.31540378859)*vv + \
         -236.890585569765)*vv + \
         -580.197272142091)*vv + \
         121.145941529601)*vv + \
         67.6766565752481)*vv + \
         -21.6329548231141)*vv + \
         2.14695963305839)*v
      complex dw = \
        (((((((((((((((((((127.043207461366*vv + \
         -188.132006786125)*vv + \
         -461.751934961566)*vv + \
         663.331673122341)*vv + \
         958.239830999318)*vv + \
         -1198.7253267254)*vv + \
         -1354.26521499883)*vv + \
         1367.66300275241)*vv + \
         1398.79606235531)*vv + \
         -1068.32881643713)*vv + \
         -1068.74261587433)*vv + \
         581.382019889864)*vv + \
         602.395750659478)*vv + \
         -217.820599435005)*vv + \
         -244.393535021604)*vv + \
         52.919720792736)*vv + \
         68.2263417416114)*vv + \
         -7.30912575066399)*vv + \
         -11.8373475755168)*vv + \
         0.358603348045432)*vv + \
         1
    endif
    sz = 7.23841523765595*(sz + nz/dz)
    sw = 140.964168155818*(sw + nw/dw)
    if @radical
      complex qrad = sqrt((((sqr(sz) - 2090)*sz + 25460)*sz - 111215)*sz + 181028)
      if |sw - qrad| < |sw + qrad|
        sw = qrad
      else
        sw = -qrad
      endif
    endif
    s = 5/(sz - 7) + 0.5
    a0 = 0.5*(((-200*sz + 8600)*sz - 55000)*sz + 72200 + 8*sqrt(5)*(sz - 17)*sw)/\
         ((((sz - 108)*sz + 3374)*sz - 24732)*sz + 52441)
    p = (s - 1)/(1 - 0.5*a0)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 22
    float w1 = 2.870250260749487538
    complex w3 = (2.87865133457600359, 1.43512513037474377)
    float sh = round(0.5*real(s)/real(w3))
    s = s - 2*w3*sh
    sh = round(0.5*imag(s)/w1)
    s = s - 2*flip(w1)*sh
    float g2 = 0.06783839755430011101
    float g3 = -0.014876800746431961231
    float c2 = g2/20
    float c3 = g3/28
    float c4 = c2*c2/3
    float c5 = 3*c2*c3/11
    float c6 = (c3*c3 + 2*c2*c4)/13
    float c7 = (c2*c5 + c3*c4)/10
    float c8 = 3*(2*c2*c6 + 2*c3*c5 + c4*c4)/85
    float c9 = (c2*c7 + c3*c6 + c4*c5)/19
    float c10 = (2*c2*c8 + 2*c3*c7 + 2*c4*c6 + c5*c5)/49
    s = s*0.25
    complex ss = sqr(s)
    complex si = 1/s
    complex ssi = sqr(si)
    complex u = ssi + \
                ((((((((c10*ss + \
                        c9)*ss + c8)*ss + c7)*ss + c6)*ss + \
                    c5)*ss + c4)*ss + c3)*ss + c2)*ss
    complex r = -2*si*ssi + \
                ((((((((18*c10*ss + \
                        16*c9)*ss + 14*c8)*ss + 12*c7)*ss + 10*c6)*ss + \
                    8*c5)*ss + 6*c4)*ss + 4*c3)*ss + 2*c2)*s
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
;    complex r1 = sqrt(4*u*u*u - 11*u/4 - 3/8)
;    if |r - r1| < |r + r1|
;      r = r1
;    else
;      r = -r1
;    endif
    r = r/sqrt(0.22556329082039276555)
    u = -u + 0.38992456788222675
    r = r/sqr(u)
    s = 1/u - 0.94696532812840456026
    a0 = (((2*s - 1)*s - 6)*s + 2 + r)*sqr(s)/\
         (((((s + 1)*s - 4)*s - 2)*s + 3)*s - 1)
    complex p = (s/(1 + s) - s)/(1 - 0.5*a0)
    a1 = s
    zd = s + p*0.5/a0
  elseif @geomtree == 21
    float w2 = 1.3728695590448768360
    float w1 = 1.5470797535511201732
    float sh = round(0.5*real(s)/w1)
    s = s - 2*w1*sh
    sh = round(0.5*imag(s)/w2)
    s = s - 2*flip(w2)*sh
    float g2 = 11/4
    float g3 = -3/8
    float c2 = g2/20
    float c3 = g3/28
    float c4 = c2*c2/3
    float c5 = 3*c2*c3/11
    float c6 = (c3*c3 + 2*c2*c4)/13
    float c7 = (c2*c5 + c3*c4)/10
    float c8 = 3*(2*c2*c6 + 2*c3*c5 + c4*c4)/85
    float c9 = (c2*c7 + c3*c6 + c4*c5)/19
    float c10 = (2*c2*c8 + 2*c3*c7 + 2*c4*c6 + c5*c5)/49
    s = s*0.25
    complex ss = sqr(s)
    complex si = 1/s
    complex ssi = sqr(si)
    complex u = ssi + \
                ((((((((c10*ss + \
                        c9)*ss + c8)*ss + c7)*ss + c6)*ss + \
                    c5)*ss + c4)*ss + c3)*ss + c2)*ss
    complex r = -2*si*ssi + \
                ((((((((18*c10*ss + \
                        16*c9)*ss + 14*c8)*ss + 12*c7)*ss + 10*c6)*ss + \
                    8*c5)*ss + 6*c4)*ss + 4*c3)*ss + 2*c2)*s
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    s = 1 - 1/(u + 5/4)
    complex t = (1 - 3*s + 2*sqr(s) + sqr(1 - s)*r)/(2*sqr(s))
    a0 = 2*s*(s*(t - 2) + 1)/(sqr(s)*(t - 1) - s + 1)
    complex p = (s - 1)/(1 - 0.5*a0)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 20
    s = 1/s
    complex t = s/(1 + s)
    complex a0 = (2*s*(s - t) - 2*sqr(s)*(s - 1))/(s - t - sqr(s)*(s - 1))
    complex p = (t - s)/(1 - 0.5*a0)
    a1 = s
    zd = a1 + p*0.5/a0
  elseif @geomtree == 19
    float w1 = 1.3254912396824867143
    complex w3 = (1.486006467050162426, 0.6627456198412433572)
    float sh = round(0.5*real(s)/real(w3))
    s = s - 2*w3*sh
    sh = round(0.5*imag(s)/w1)
    s = s - 2*flip(w1)*sh
    float g2 = 450/216
    float g3 = -253/216
    float c2 = g2/20
    float c3 = g3/28
    float c4 = c2*c2/3

    float c5 = 3*c2*c3/11
    float c6 = (c3*c3 + 2*c2*c4)/13
    float c7 = (c2*c5 + c3*c4)/10
    float c8 = 3*(2*c2*c6 + 2*c3*c5 + c4*c4)/85
    float c9 = (c2*c7 + c3*c6 + c4*c5)/19
    float c10 = (2*c2*c8 + 2*c3*c7 + 2*c4*c6 + c5*c5)/49
    s = s*0.25
    complex ss = sqr(s)
    complex si = 1/s
    complex ssi = sqr(si)
    complex u = ssi + \
                ((((((((c10*ss + \
                        c9)*ss + c8)*ss + c7)*ss + c6)*ss + \
                    c5)*ss + c4)*ss + c3)*ss + c2)*ss
    complex r = -2*si*ssi + \
                ((((((((18*c10*ss + \
                        16*c9)*ss + 14*c8)*ss + 12*c7)*ss + 10*c6)*ss + \
                    8*c5)*ss + 6*c4)*ss + 4*c3)*ss + 2*c2)*s
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
;    complex r1 = sqrt(4*u*u*u - 11*u/4 - 3/8)
;    if |r - r1| < |r + r1|
;      r = r1
;    else
;      r = -r1
;    endif
    s = 2*(111 - 36*(u + r))/((144*u + 120)*u + 277)
    a0 = -u + 13/12
    complex p = (s - 1)/(1 - 0.5*a0)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 18
    complex u = s
    complex a0 = (1 - 4*sqr(u))*0.5
    complex p = -4/((4*u + 4)*u + 5)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 17
    complex a0 = 1/s + 1
    complex p = 1/(a0 - 2)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 16
    complex t = 1/s + 1
    a0 = 2*t*((t - 1)*t + 1)/(((t - 1)*t + 1)*t + 1)
    complex p = (((t - 2)*t + 2)*sqr(t) - 1)/((t - 2)*t + 2)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 15
    s = flip(1)*s
    float w1 = 1.3728695590448768360
    float w2 = 1.5470797535511201732
    float sh = round(0.5*real(s)/w1)
    s = s - 2*w1*sh
    sh = round(0.5*imag(s)/w2)
    s = s - 2*flip(w2)*sh
    float g2 = 11/4
    float g3 = 3/8
    float c2 = g2/20
    float c3 = g3/28
    float c4 = c2*c2/3
    float c5 = 3*c2*c3/11
    float c6 = (c3*c3 + 2*c2*c4)/13
    float c7 = (c2*c5 + c3*c4)/10
    float c8 = 3*(2*c2*c6 + 2*c3*c5 + c4*c4)/85
    float c9 = (c2*c7 + c3*c6 + c4*c5)/19
    float c10 = (2*c2*c8 + 2*c3*c7 + 2*c4*c6 + c5*c5)/49
    s = s*0.25
    complex ss = sqr(s)
    complex si = 1/s
    complex ssi = sqr(si)
    complex u = ssi + \
                ((((((((c10*ss + \
                        c9)*ss + c8)*ss + c7)*ss + c6)*ss + \
                    c5)*ss + c4)*ss + c3)*ss + c2)*ss
    complex r = -2*si*ssi + \
                ((((((((18*c10*ss + \
                        16*c9)*ss + 14*c8)*ss + 12*c7)*ss + 10*c6)*ss + \
                    8*c5)*ss + 6*c4)*ss + 4*c3)*ss + 2*c2)*s
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
;    complex r1 = sqrt(4*u*u*u - 11*u/4 - 3/8)
;    if |r - r1| < |r + r1|
;      r = r1
;    else
;      r = -r1
;    endif
    complex t = (flip(8)*r - 9 + 16*sqr(u))/(16*sqr(u) + 8*u -19)
    s = 1/(u - 5/4) + 1
    complex p = (sqr(t) + s - 1)/(1 - t)
    a0 = 2*(1 + (1 - s)/p)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 14
    s = 1/s
    a1 = 0
    a0 = 1
    complex p = s
    zd = p*0.5/a0
  elseif @geomtree == 13
    s = 1/s + 0.5*(3 - sqrt(5))
    complex a0 = (4*sqr(s) - 2*s)/(s - 1 + sqr(s))
    complex p = (s - 1)/(1 - 0.5*a0)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 12
    complex p = -1/(1 - 0.5*s)
    complex a0 = s
    zd = 1 + p*0.5/a0
  elseif @geomtree == 11
    s = sqrt(s)
    complex a0 = s
    complex ss = sqr(s)
    complex b = (sqr(sqr(ss)) - 1)/(2*s*ss*(ss - 1))
    complex p = 0.5*(sqrt(sqr(b) - 4) - b)
    complex a1 = s*p
    p = p - ss*p
    zd = a0
  elseif @geomtree == 10
    s = 1/s + 1
    complex p = 4*s*(s - 1)/(2 - s)
    complex a0 = s
    zd = 1 + p*0.5/a0
  elseif @geomtree == 9
    s = 1/s + 1
    complex p = (s - 1)/(1 - 0.5*s)
    complex a0 = s
    zd = 1 + p*0.5/a0
  elseif @geomtree == 8
    complex p = -1
    complex a0 = s
    zd = 1 + p*0.5/a0
  elseif @geomtree == 7
    s = 1/s + 1
    complex p = sqr(s) - 1
    complex a0 = 2*s/(s + 1)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 6
    s = 1/s + 4
    complex p = s
    complex a0 = 2
    zd = 1 + p*0.25
  elseif @geomtree == 5
    s = 1/s
    complex p = s
    complex a0 = 1
    zd = 1 + p*0.5
  elseif @geomtree == 4
    if @insout
      s = 1/s
    endif
    complex a0 = s
    complex p = -2*s
    zd = 1
  elseif @geomtree == 3
    complex p = s
    complex a0 = sqrt(1 + 4*sqr(p))
    zd = 2*p + a0
    zd = (zd + 1/zd)*p + a0
  elseif @geomtree == 2
    s = (1 - s)/(1 + s)
    complex p = (1 - s)/(s + 1/s + 2)
    complex a0 = s + 2*p
    zd = 2*p + a0
  elseif @geomtree == 1
    complex p = s
    complex a0 = 1 + 2*s
    zd = 2*p + a0
  else
    complex p = s
    complex a0 = 0
    zd = 2*p + a0
  endif
  complex pd = @windage*p/sqrt(2)
  z = @bailout
loop:
  if @geomtree == 11
    complex zi = 1/(sqr(zd) + a1)
  else
    complex zi = 1/zd

  endif
  if @geomtree <= 3
    z = z*pd*(1 - sqr(zi))
    zd = (zd + zi)*p + a0
  elseif @geomtree == 11
    z = -z*pd*2*zd*sqr(zi)
    zd = a0 + p*zi
  else
    z = z*pd*sqr(zi)*(a0*zi - 1)
    zd = a1 + p*zi*(1 - 0.5*a0*zi)
  endif
bailout:
  |z| > |zd|
default:
  title = "Quad2crit"

  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."
  endparam
  param hypcent
    caption = "Hyperbolic Translation"
    default = (1,1)
    hint = "Move the origin around by a horizontal move followed \
            by vertical move. (1, 2.85042103537095), (1, 1), \
            (3.36274791875425, 1),  (13.53249303123686, 2.85042103537095) \
            center 4 of 6 Weierstrass points."
  endparam
  param uhp
    caption = "Half Plane"
    default = false
    hint = "half plane model of hyperbolic plane"
  endparam
  param radical
    caption = "Radical"
    default = false
    hint = "From a purist standpoint this is unnecessary.  It helps \
            coherence on zooms deeper than 1e8."
  endparam
  param n
    caption = "Order"
    default = 3
    hint = "This defines the order of the Chebyshev polynomial."
  endparam
  param nd
    caption = "Destination"
    default = 0
    hint = "This defines the destination critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param coslimit
    caption = "Cosine limit"
    default = false
    hint = "As order approaches infinity we get a cosine \
            with chained critical points."
  endparam
  param fold
    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0."
  endparam
  param windage
    caption = "Kentucky"
    default = 1.0
    hint = "Windage for the convergance criteria."
  endparam
  param bailout
    caption = "Bailout value"
    default = 1e24
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:

  type = "Juad2crit"

  seed = #pixel
  power = power
  n = n
  nd = nd
  radical = radical
  hypcent = hypcent
  coslimit = coslimit
  geomtree = geomtree
  windage = windage
  lowfix = lowfix
  insout = insout
  fold = fold
  bailout = bailout
}


Juad2crit {

; Generic Julia set
init:
  complex s = @seed
  complex a0 = 0
  complex a1 = 1
  if @geomtree == 23
    complex u = s
    float hr = real(@hypcent)
    float hi = imag(@hypcent)
    u = ((hr + 1)*u + (hr - 1))/((hr - 1)*u + (hr + 1))
    u = ((hi + 1)*u + flip(hi - 1))/(-flip(hi - 1)*u + (hi + 1))
    if |u| > 1
      u = 1/u
    endif
    complex fu00 = (1.83006188130296, 0)
    complex fu01 = (1.53268603745129, 0)
    complex fu02 = (1.53268603745129, 0)
    complex fu03 = (1.83006188130296, 0)
    complex fu10 = (4.97479722366339, 0)
    complex fu11 = (3.49069798919486, 3.40053451163194)
    complex fu12 = (3.49069798919486, -3.40053451163194)
    complex fu13 = (4.97479722366339, 0)
    complex fu20 = (1.60062320016132, 0)
    complex fu21 = (0, 1.24979783520963)
    complex fu22 = (0, -1.24979783520963)
    complex fu23 = (1.60062320016132, 0)
    complex fu30 = (4.97479722366339, 0)
    complex fu31 = (-3.49069798919486, 3.40053451163194)
    complex fu32 = (-3.49069798919486, -3.40053451163194)
    complex fu33 = (4.97479722366339, 0)
    complex fu40 = (1.83006188130296, 0)
    complex fu41 = (-1.53268603745129, 0)
    complex fu42 = (-1.53268603745129, 0)
    complex fu43 = (1.83006188130296, 0)
    complex fu50 = (4.97479722366339, 0)
    complex fu51 = (-3.49069798919486, -3.40053451163194)
    complex fu52 = (-3.49069798919486, 3.40053451163194)
    complex fu53 = (4.97479722366339, 0)
    complex fu60 = (1.60062320016132, 0)
    complex fu61 = (0, -1.24979783520963)
    complex fu62 = (0, 1.24979783520963)
    complex fu63 = (1.60062320016132, 0)
    complex fu70 = (4.97479722366339, 0)
    complex fu71 = (3.49069798919486, -3.40053451163194)
    complex fu72 = (3.49069798919486, 3.40053451163194)
    complex fu73 = (4.97479722366339, 0)
    complex vu00 = (-6.80319462258186, 0)
    complex vu01 = (-6.729298408655, 0)
    complex vu02 = (-6.729298408655, 0)
    complex vu03 = (-6.80319462258186, 0)
    complex vu10 = (-1.7689197870267, 0)
    complex vu11 = (-1.23660891469389, 0.774516368474021)
    complex vu12 = (-1.23660891469389, -0.774516368474021)
    complex vu13 = (-1.7689197870267, 0)
    complex vu20 = (-3.6669160814782, 0)
    complex vu21 = (0, 3.52792765637327)
    complex vu22 = (0, -3.52792765637327)
    complex vu23 = (-3.6669160814782, 0)
    complex vu30 = (-1.7689197870267, 0)
    complex vu31 = (1.2366089146939, 0.774516368474026)
    complex vu32 = (1.2366089146939, -0.774516368474026)
    complex vu33 = (-1.7689197870267, 0)
    complex vu40 = (-6.80319462258187, 0)
    complex vu41 = (6.72929840865501, 0)
    complex vu42 = (6.72929840865501, 0)
    complex vu43 = (-6.80319462258187, 0)
    complex vu50 = (-1.7689197870267, 0)
    complex vu51 = (1.23660891469389, -0.774516368474024)
    complex vu52 = (1.23660891469389, 0.774516368474024)
    complex vu53 = (-1.7689197870267, 0)
    complex vu60 = (-3.6669160814782, 0)
    complex vu61 = (0, -3.52792765637328)
    complex vu62 = (0, 3.52792765637328)
    complex vu63 = (-3.6669160814782, 0)
    complex vu70 = (-1.7689197870267, 0)
    complex vu71 = (-1.2366089146939, -0.77451636847402)
    complex vu72 = (-1.2366089146939, 0.77451636847402)
    complex vu73 = (-1.7689197870267, 0)
    complex umata = (1.81711731221675, 0.743926303451645)
    complex umatb = (-0.984102273962777, -1.37363910315131)
    complex umatc = (-0.984102273962777, 1.37363910315131)
    complex umatd = (1.81711731221675, -0.743926303451645)
    complex ffun = (0.775238238163461, 0.66715237172243)
    float ffnm = 0.0460866130
    complex vfun = (0.915597613665918, 0.822040232602688)
    float vfnm = 0.5140691341
    bool better = true
    complex t = 0
    while better
      better = false
      t = (fu00*u + fu01)/(fu02*u + fu03)
      if |t| < |u|
        better = true
        u = t
      endif
      t = (fu10*u + fu11)/(fu12*u + fu13)
      if |u + ffun| < ffnm
        better = true
        u = t
      endif
      t = (fu20*u + fu21)/(fu22*u + fu23)
      if |t| < |u|
        better = true
        u = t
      endif
      t = (fu30*u + fu31)/(fu32*u + fu33)
      if |u - conj(ffun)| < ffnm
        better = true
        u = t
      endif
      t = (fu40*u + fu41)/(fu42*u + fu43)
      if |t| < |u|
        better = true
        u = t
      endif
      t = (fu50*u + fu51)/(fu52*u + fu53)
      if |u - ffun| < ffnm
        better = true
        u = t
      endif
      t = (fu60*u + fu61)/(fu62*u + fu63)
      if |t| < |u|
        better = true
        u = t
      endif
      t = (fu70*u + fu71)/(fu72*u + fu73)
      if |u + conj(ffun)| < ffnm
        better = true
        u = t
      endif
    endwhile
    complex v = (umata*u + umatb)/(umatc*u + umatd)
    better = true
    while better
      better = false
      t = (vu00*v + vu01)/(vu02*v + vu03)
      if |t| < |v|
        better = true
        v = t
      endif
      t = (vu10*v + vu11)/(vu12*v + vu13)
      if |v + conj(vfun)| < vfnm
        better = true
        v = t
      endif
      t = (vu20*v + vu21)/(vu22*v + vu23)
      if |t| < |v|
        better = true
        v = t
      endif
      t = (vu30*v + vu31)/(vu32*v + vu33)
      if |v - vfun| < vfnm
        better = true
        v = t
      endif
      t = (vu40*v + vu41)/(vu42*v + vu43)
      if |t| < |v|
        better = true
        v = t
      endif
      t = (vu50*v + vu51)/(vu52*v + vu53)
      if |v - conj(vfun)| < vfnm
        better = true
        v = t
      endif
      t = (vu60*v + vu61)/(vu62*v + vu63)
      if |t| < |v|
        better = true
        v = t
      endif
      t = (vu70*v + vu71)/(vu72*v + vu73)
      if |v + vfun| < vfnm
        better = true
        v = t
      endif
    endwhile
    if |v| > |u|
      complex uu = u*u
      complex sz = \
        ((((((((((((((((((((((((((((((50.8285043301517*uu + \
         21.1822729720076)*uu + \
         16.765948907338)*uu + \
         43.7961380207474)*uu + \
         1.50138455967125)*uu + \
         27.1782031497161)*uu + \
         -7.44269317223692)*uu + \
         -0.226471541200099)*uu + \
         3.63505365756027)*uu + \
         -20.2540399540202)*uu + \
         -0.954747741789354)*uu + \
         -20.8675379240415)*uu + \
         1.99779330425055)*uu + \
         -12.1941098477131)*uu + \
         -3.14790838392742)*uu + \
         1.49016780408159)*uu + \
         -2.15269122870894)*uu + \
         5.29090496756078)*uu + \
         -0.544075835468025)*uu + \
         4.7195308772554)*uu + \
         4.53089725317355)*uu + \
         1.96072189949404)*uu + \
         3.84622774686998)*uu + \
         -1.12491301047044)*uu + \
         3.1611075885776)*uu + \
         -1.48090275608658)*uu + \
         0.265955064052117)*uu + \
         -0.914809768957607)*uu + \
         -0.80558574702971)*uu + \
         -0.43271738253076)*uu + \
         -0.948850047211325)*uu + \
         -0.266318358487369
      complex nz = \
        ((((3.34932481372634*uu + \
         -2.29108516679601)*uu + \
         -3.56428044938751)*uu + \
         3.17921539381276)*uu + \
         0.429033840461224)*uu + \
         1
      complex dz = \
        ((((5.4682410869534*uu + \
         -1.00326433962286)*uu + \
         -4.63083659896653)*uu + \
         0.429033840461224)*uu + \
         1)*uu
      complex sw = \
        (((((((((((((((((((((((((((((((1244.55156098388*uu + \
         -1044.85318148304)*uu + \
         1365.11006115432)*uu + \
         734.195716441453)*uu + \
         710.618884533585)*uu + \
         1358.98468918307)*uu + \
         15.7112863617801)*uu + \
         1060.64875311286)*uu + \
         -123.815283338864)*uu + \
         326.295201175061)*uu + \
         -111.590370800305)*uu + \
         -204.712545025044)*uu + \
         -25.2704061171468)*uu + \
         -328.32887144145)*uu + \
         -76.399453271931)*uu + \
         -196.33361527777)*uu + \
         -81.7934486435375)*uu + \
         -31.843023775531)*uu + \
         -77.2679391900259)*uu + \
         57.5337428147105)*uu + \
         -26.495947466048)*uu + \
         57.9291962404693)*uu + \
         7.28566661633742)*uu + \
         28.7609465707033)*uu + \
         22.536642650597)*uu + \
         8.788506347703)*uu + \
         12.0922840394811)*uu + \
         -0.831988373488552)*uu + \
         1.52752556995338)*uu + \
         -1.18976521806274)*uu + \
         -4.12466463652027)*uu + \
         -0.547056822581384)*u
      complex nw = \
        (((((((((((229.924588338754*uu + \
         -88.0861356394314)*uu + \
         -397.88217487117)*uu + \
         109.673495603488)*uu + \
         246.508977532891)*uu + \
         -38.4869271353045)*uu + \
         -40.9069618845349)*uu + \
         -1.05742260136996)*uu + \
         -5.387448424406)*uu + \
         8.74182600327833)*uu + \
         -14.6048749660359)*uu + \
         0.406788704973983)*uu + \
         1
      complex dw = \
        ((((((((((-69.9228520720704*uu + \
         32.0720606924251)*uu + \
         143.624005894562)*uu + \
         -54.3211135343213)*uu + \
         -120.346543338335)*uu + \
         34.7296841165408)*uu + \
         51.4647412805411)*uu + \
         -9.93392805301499)*uu + \
         -11.2319601794271)*uu + \
         1.07258460115308)*uu + \
         1)*uu*uu*u
    else
      complex vv = v*v
      complex sz = \
        ((((((((((((((((((((((((((((((-329.896829137034*vv + \
         535.632662850714)*vv + \
         -288.859170603267)*vv + \
         -136.186896677415)*vv + \
         283.761403759031)*vv + \
         -217.930463962149)*vv + \
         -23.5363445826578)*vv + \
         171.955234482815)*vv + \
         -124.314467349942)*vv + \
         25.6165980308276)*vv + \
         85.6870647250078)*vv + \
         -88.060327555702)*vv + \
         26.8279872568985)*vv + \
         26.7712280038119)*vv + \
         -58.9580364407965)*vv + \
         18.0525146698689)*vv + \
         13.7677240678965)*vv + \
         -26.0102371357958)*vv + \
         19.4593783521772)*vv + \
         7.19940203377203)*vv + \
         -13.4112462232443)*vv + \
         14.0437317095019)*vv + \
         -0.927034606640644)*vv + \
         -8.0940195654052)*vv + \
         4.36962946466608)*vv + \
         -2.00770760225374)*vv + \
         -3.26524229220525)*vv + \
         3.114507368033)*vv + \
         -0.477293557447735)*vv + \
         -0.634207615660206)*vv + \
         2.02989764260562)*vv + \
         0.730031515734547
      complex nz = \
        (((((((-4.99606287451219*vv + \
         2.81979769244912)*vv + \
         9.37398018603044)*vv + \
         -4.90048917295332)*vv + \
         -9.8354733320135)*vv + \
         7.18033780423563)*vv + \
         4.47509521442272)*vv + \
         -4.33082353513855)*vv
      complex dz = \
        (((((((6.94353421608628*vv + \
         -4.11293465385055)*vv + \
         -11.9219954315396)*vv + \
         4.08930170614781)*vv + \
         10.8119014669575)*vv + \
         -1.90191994136891)*vv + \
         -4.75037059355414)*vv + \
         0.143441339218172)*vv + \
         1
      complex sw = \
        (((((((((((((((((((((((((((((((-93431.4994472434*vv + \
         58158.071042987)*vv + \
         8798.90521834021)*vv + \
         -41533.5615653787)*vv + \
         32872.5932348587)*vv + \
         -3114.45150978675)*vv + \
         -17679.9057595404)*vv + \
         16558.9464899814)*vv + \
         -4762.53420355266)*vv + \
         -6531.3413236715)*vv + \
         8166.50724876673)*vv + \
         -3113.82729701504)*vv + \
         -1797.28687520996)*vv + \
         3756.97369928781)*vv + \
         -1903.94716932743)*vv + \
         -372.84232513744)*vv + \
         1407.02718322058)*vv + \
         -1055.56571478838)*vv + \
         -29.2877696137142)*vv + \
         485.543604170474)*vv + \
         -441.109754141229)*vv + \
         92.5527983672403)*vv + \
         178.668067972833)*vv + \
         -161.840442962114)*vv + \
         70.0359016559377)*vv + \
         38.5132396817261)*vv + \
         -55.6468209924833)*vv + \
         17.4224965414547)*vv + \
         2.07279297810727)*vv + \
         -16.5157882429291)*vv + \
         6.21879960338274)*vv + \
         1.19457099958621)*v
      complex nw = \
        (((((((((((((((((((-262.016818978863*vv + \
         799.2917646746)*vv + \
         342.79241953858)*vv + \
         -2709.02794743515)*vv + \
         -75.7903919274321)*vv + \
         5154.96845769143)*vv + \
         -341.050352953843)*vv + \
         -6587.67925347603)*vv + \
         452.832004767186)*vv + \
         6127.3192751211)*vv + \
         -384.03255866431)*vv + \
         -4143.63025839381)*vv + \
         301.635914862471)*vv + \
         1972.31540378859)*vv + \
         -236.890585569765)*vv + \
         -580.197272142091)*vv + \
         121.145941529601)*vv + \
         67.6766565752481)*vv + \
         -21.6329548231141)*vv + \
         2.14695963305839)*v
      complex dw = \
        (((((((((((((((((((127.043207461366*vv + \
         -188.132006786125)*vv + \
         -461.751934961566)*vv + \
         663.331673122341)*vv + \
         958.239830999318)*vv + \
         -1198.7253267254)*vv + \
         -1354.26521499883)*vv + \
         1367.66300275241)*vv + \
         1398.79606235531)*vv + \
         -1068.32881643713)*vv + \
         -1068.74261587433)*vv + \
         581.382019889864)*vv + \
         602.395750659478)*vv + \
         -217.820599435005)*vv + \
         -244.393535021604)*vv + \
         52.919720792736)*vv + \
         68.2263417416114)*vv + \
         -7.30912575066399)*vv + \
         -11.8373475755168)*vv + \
         0.358603348045432)*vv + \
         1
    endif
    sz = 7.23841523765595*(sz + nz/dz)
    sw = 140.964168155818*(sw + nw/dw)
    if @radical
      complex qrad = sqrt((((sqr(sz) - 2090)*sz + 25460)*sz - 111215)*sz + 181028)
      if |sw - qrad| < |sw + qrad|
        sw = qrad
      else
        sw = -qrad
      endif
    endif
    s = 5/(sz - 7) + 0.5
    a0 = 0.5*(((-200*sz + 8600)*sz - 55000)*sz + 72200 + 8*sqrt(5)*(sz - 17)*sw)/\
         ((((sz - 108)*sz + 3374)*sz - 24732)*sz + 52441)
    p = (s - 1)/(1 - 0.5*a0)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 22
    float w1 = 2.870250260749487538
    complex w3 = (2.87865133457600359, 1.43512513037474377)
    float sh = round(0.5*real(s)/real(w3))
    s = s - 2*w3*sh
    sh = round(0.5*imag(s)/w1)
    s = s - 2*flip(w1)*sh
    float g2 = 0.06783839755430011101
    float g3 = -0.014876800746431961231
    float c2 = g2/20
    float c3 = g3/28
    float c4 = c2*c2/3
    float c5 = 3*c2*c3/11
    float c6 = (c3*c3 + 2*c2*c4)/13
    float c7 = (c2*c5 + c3*c4)/10
    float c8 = 3*(2*c2*c6 + 2*c3*c5 + c4*c4)/85
    float c9 = (c2*c7 + c3*c6 + c4*c5)/19
    float c10 = (2*c2*c8 + 2*c3*c7 + 2*c4*c6 + c5*c5)/49
    s = s*0.25
    complex ss = sqr(s)
    complex si = 1/s
    complex ssi = sqr(si)
    complex u = ssi + \
                ((((((((c10*ss + \
                        c9)*ss + c8)*ss + c7)*ss + c6)*ss + \
                    c5)*ss + c4)*ss + c3)*ss + c2)*ss
    complex r = -2*si*ssi + \
                ((((((((18*c10*ss + \
                        16*c9)*ss + 14*c8)*ss + 12*c7)*ss + 10*c6)*ss + \
                    8*c5)*ss + 6*c4)*ss + 4*c3)*ss + 2*c2)*s
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
;    complex r1 = sqrt(4*u*u*u - 11*u/4 - 3/8)
;    if |r - r1| < |r + r1|
;      r = r1
;    else
;      r = -r1
;    endif
    r = r/sqrt(0.22556329082039276555)
    u = -u + 0.38992456788222675
    r = r/sqr(u)
    s = 1/u - 0.94696532812840456026
    a0 = (((2*s - 1)*s - 6)*s + 2 + r)*sqr(s)/\
         (((((s + 1)*s - 4)*s - 2)*s + 3)*s - 1)
    complex p = (s/(1 + s) - s)/(1 - 0.5*a0)
    a1 = s
    zd = s + p*0.5/a0
  elseif @geomtree == 21
    float w2 = 1.3728695590448768360
    float w1 = 1.5470797535511201732
    float sh = round(0.5*real(s)/w1)
    s = s - 2*w1*sh
    sh = round(0.5*imag(s)/w2)
    s = s - 2*flip(w2)*sh
    float g2 = 11/4
    float g3 = -3/8
    float c2 = g2/20
    float c3 = g3/28
    float c4 = c2*c2/3
    float c5 = 3*c2*c3/11
    float c6 = (c3*c3 + 2*c2*c4)/13
    float c7 = (c2*c5 + c3*c4)/10
    float c8 = 3*(2*c2*c6 + 2*c3*c5 + c4*c4)/85
    float c9 = (c2*c7 + c3*c6 + c4*c5)/19
    float c10 = (2*c2*c8 + 2*c3*c7 + 2*c4*c6 + c5*c5)/49
    s = s*0.25
    complex ss = sqr(s)
    complex si = 1/s
    complex ssi = sqr(si)
    complex u = ssi + \
                ((((((((c10*ss + \
                        c9)*ss + c8)*ss + c7)*ss + c6)*ss + \
                    c5)*ss + c4)*ss + c3)*ss + c2)*ss
    complex r = -2*si*ssi + \
                ((((((((18*c10*ss + \
                        16*c9)*ss + 14*c8)*ss + 12*c7)*ss + 10*c6)*ss + \
                    8*c5)*ss + 6*c4)*ss + 4*c3)*ss + 2*c2)*s
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    s = 1 - 1/(u + 5/4)
    complex t = (1 - 3*s + 2*sqr(s) + sqr(1 - s)*r)/(2*sqr(s))
    a0 = 2*s*(s*(t - 2) + 1)/(sqr(s)*(t - 1) - s + 1)
    complex p = (s - 1)/(1 - 0.5*a0)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 20
    s = 1/s
    complex t = s/(1 + s)
    complex a0 = (2*s*(s - t) - 2*sqr(s)*(s - 1))/(s - t - sqr(s)*(s - 1))
    complex p = (t - s)/(1 - 0.5*a0)
    a1 = s
    zd = a1 + p*0.5/a0
  elseif @geomtree == 19
    float w1 = 1.3254912396824867143
    complex w3 = (1.486006467050162426, 0.6627456198412433572)
    float sh = round(0.5*real(s)/real(w3))
    s = s - 2*w3*sh
    sh = round(0.5*imag(s)/w1)
    s = s - 2*flip(w1)*sh
    float g2 = 450/216
    float g3 = -253/216
    float c2 = g2/20
    float c3 = g3/28
    float c4 = c2*c2/3
    float c5 = 3*c2*c3/11
    float c6 = (c3*c3 + 2*c2*c4)/13
    float c7 = (c2*c5 + c3*c4)/10
    float c8 = 3*(2*c2*c6 + 2*c3*c5 + c4*c4)/85
    float c9 = (c2*c7 + c3*c6 + c4*c5)/19
    float c10 = (2*c2*c8 + 2*c3*c7 + 2*c4*c6 + c5*c5)/49
    s = s*0.25
    complex ss = sqr(s)
    complex si = 1/s
    complex ssi = sqr(si)
    complex u = ssi + \
                ((((((((c10*ss + \
                        c9)*ss + c8)*ss + c7)*ss + c6)*ss + \
                    c5)*ss + c4)*ss + c3)*ss + c2)*ss
    complex r = -2*si*ssi + \
                ((((((((18*c10*ss + \
                        16*c9)*ss + 14*c8)*ss + 12*c7)*ss + 10*c6)*ss + \
                    8*c5)*ss + 6*c4)*ss + 4*c3)*ss + 2*c2)*s
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
;    complex r1 = sqrt(4*u*u*u - 11*u/4 - 3/8)
;    if |r - r1| < |r + r1|
;      r = r1
;    else
;      r = -r1
;    endif
    s = 2*(111 - 36*(u + r))/((144*u + 120)*u + 277)
    a0 = -u + 13/12
    complex p = (s - 1)/(1 - 0.5*a0)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 18
    complex u = s
    complex a0 = (1 - 4*sqr(u))*0.5
    complex p = -4/((4*u + 4)*u + 5)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 17
    complex a0 = 1/s + 1

    complex p = 1/(a0 - 2)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 16
    complex t = 1/s + 1
    a0 = 2*t*((t - 1)*t + 1)/(((t - 1)*t + 1)*t + 1)
    complex p = (((t - 2)*t + 2)*sqr(t) - 1)/((t - 2)*t + 2)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 15
    s = flip(1)*s
    float w1 = 1.3728695590448768360
    float w2 = 1.5470797535511201732
    float sh = round(0.5*real(s)/w1)
    s = s - 2*w1*sh
    sh = round(0.5*imag(s)/w2)
    s = s - 2*flip(w2)*sh
    float g2 = 11/4
    float g3 = 3/8
    float c2 = g2/20
    float c3 = g3/28
    float c4 = c2*c2/3
    float c5 = 3*c2*c3/11
    float c6 = (c3*c3 + 2*c2*c4)/13
    float c7 = (c2*c5 + c3*c4)/10
    float c8 = 3*(2*c2*c6 + 2*c3*c5 + c4*c4)/85
    float c9 = (c2*c7 + c3*c6 + c4*c5)/19
    float c10 = (2*c2*c8 + 2*c3*c7 + 2*c4*c6 + c5*c5)/49
    s = s*0.25
    complex ss = sqr(s)
    complex si = 1/s
    complex ssi = sqr(si)
    complex u = ssi + \
                ((((((((c10*ss + \
                        c9)*ss + c8)*ss + c7)*ss + c6)*ss + \
                    c5)*ss + c4)*ss + c3)*ss + c2)*ss
    complex r = -2*si*ssi + \
                ((((((((18*c10*ss + \
                        16*c9)*ss + 14*c8)*ss + 12*c7)*ss + 10*c6)*ss + \
                    8*c5)*ss + 6*c4)*ss + 4*c3)*ss + 2*c2)*s
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
    complex q = 6*sqr(u) - 0.5*g2
    complex r1 = 0.25*q*(12*sqr(r)*u - sqr(q))/(r*sqr(r)) - r
    u = 0.25*sqr(q/r) - 2*u
    r = r1
;    complex r1 = sqrt(4*u*u*u - 11*u/4 - 3/8)
;    if |r - r1| < |r + r1|
;      r = r1
;    else
;      r = -r1
;    endif
    complex t = (flip(8)*r - 9 + 16*sqr(u))/(16*sqr(u) + 8*u -19)
    s = 1/(u - 5/4) + 1
    complex p = (sqr(t) + s - 1)/(1 - t)
    a0 = 2*(1 + (1 - s)/p)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 14
    s = 1/s
    a1 = 0
    a0 = 1
    complex p = s
    zd = p*0.5/a0
  elseif @geomtree == 13
    s = 1/s + 0.5*(3 - sqrt(5))
    complex a0 = (4*sqr(s) - 2*s)/(s - 1 + sqr(s))
    complex p = (s - 1)/(1 - 0.5*a0)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 12
    complex p = -1/(1 - 0.5*s)
    complex a0 = s
    zd = 1 + p*0.5/a0
  elseif @geomtree == 11
    s = sqrt(s)
    complex a0 = s
    complex ss = sqr(s)
    complex b = (sqr(sqr(ss)) - 1)/(2*s*ss*(ss - 1))
    complex p = 0.5*(sqrt(sqr(b) - 4) - b)
    complex a1 = s*p
    p = p - ss*p
    zd = a0
  elseif @geomtree == 10
    s = 1/s + 1
    complex p = 4*s*(s - 1)/(2 - s)
    complex a0 = s
    zd = 1 + p*0.5/a0
  elseif @geomtree == 9
    s = 1/s + 1
    complex p = (s - 1)/(1 - 0.5*s)
    complex a0 = s
    zd = 1 + p*0.5/a0
  elseif @geomtree == 8
    complex p = -1
    complex a0 = s
    zd = 1 + p*0.5/a0
  elseif @geomtree == 7
    s = 1/s + 1
    complex p = sqr(s) - 1
    complex a0 = 2*s/(s + 1)
    zd = 1 + p*0.5/a0
  elseif @geomtree == 6
    s = 1/s + 4
    complex p = s
    complex a0 = 2
    zd = 1 + p*0.25
  elseif @geomtree == 5
    s = 1/s
    complex p = s
    complex a0 = 1
    zd = 1 + p*0.5
  elseif @geomtree == 4

    if @insout
      s = 1/s
    endif
    complex a0 = s
    complex p = -2*s
    zd = 1
  elseif @geomtree == 3
    complex p = s
    complex a0 = sqrt(1 + 4*sqr(p))
    zd = 2*p + a0
    zd = (zd + 1/zd)*p + a0
  elseif @geomtree == 2
    s = (1 - s)/(1 + s)
    complex p = (1 - s)/(s + 1/s + 2)
    complex a0 = s + 2*p
    zd = 2*p + a0
  elseif @geomtree == 1
    complex p = s
    complex a0 = 1 + 2*s
    zd = 2*p + a0
  else
    complex p = s
    complex a0 = 0
    zd = 2*p + a0
  endif
  complex pd = @windage*p/sqrt(2)
  z = @bailout
  zd = #pixel
  if (@geomtree == 6) || (@geomtree == 7) || (@geomtree == 8) || \
     (@geomtree == 16) || (@geomtree == 17) || (@geomtree == 18) || \
     (@geomtree == 20) || (@geomtree == 21) || (@geomtree == 22) || \
     (@geomtree == 23)
    zd = 1/zd + a0
  endif
  if (@geomtree == 12) || (@geomtree == 13) || (@geomtree == 15) || \
     (@geomtree == 19)
    zd = 1/zd
  endif
loop:
  if @geomtree == 11
    complex zi = 1/(sqr(zd) + a1)
  else
    complex zi = 1/zd
  endif
  if @geomtree <= 3
    z = z*pd*(1 - sqr(zi))
    zd = (zd + zi)*p + a0
  elseif @geomtree == 11
    z = -z*pd*2*zd*sqr(zi)
    zd = a0 + p*zi
  else
    z = z*pd*sqr(zi)*(a0*zi - 1)
    zd = a1 + p*zi*(1 - 0.5*a0*zi)
  endif
bailout:
  |z| > |zd|
default:
  title = "Juad2crit"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param hypcent
    caption = "Hyperbolic Translation"
    default = (1,1)
    hint = "Move the origin around by a horizontal move followed \
            by vertical move. (1, 2.85042103537095), (1, 1), \
            (3.36274791875425, 1),  (13.53249303123686, 2.85042103537095) \
            center 4 of 6 Weierstrass points."
  endparam
  param radical
    caption = "Radical"
    default = false
    hint = "From a purist standpoint this is unnecessary.  It helps \
            coherence on zooms deeper than 1e8."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param nd
    caption = "Destination"
    default = 0
    hint = "This defines the destination critical point."
  endparam
  param insout

    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param fold
    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0."
  endparam
  param coslimit
    caption = "Cosine limit"
    default = false
    hint = "As order approaches infinity we get a cosine \
            with chained critical points."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param windage
    caption = "Kentucky"
    default = 1.0
    hint = "Windage for the convergance criteria."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Quad2crit"
  power = power
  bailout = bailout
}

Chebcheb {
; Generic Mandelbrot set
init:
  complex s = #pixel
  complex t = 0
  complex u = 0
  int usign = 1
  complex r = 0
  int rsign = 1
  if @coslimit
    t = #pi*@ne
  else
    complex u = cos(@nd*#pi/@n)
    if floor(0.5*@nd) == 0.5*@nd
      int usign = 1
    else
      int usign = -1
    endif

    complex t = cos(@ne*#pi/@n)
  endif
  if !@coslimit2
    complex r = cos(@nf*#pi/@n2)
    if floor(0.5*@nf) == 0.5*@nf
      int rsign = 1
    else
      int rsign = -1
    endif
  endif
  if @insout
    s = 1/s + 1
  endif
  if @fold
    if @coslimit && (floor(0.5*@ne) == 0.5*@ne) && \

       (@n2 == 2) && (@nf == 1) && (@geomtree == 0)
      s = (1/s + 1)*sqr(@ne)
    elseif @coslimit && (floor(0.5*@ne) != 0.5*@ne) && \
       (@n2 == 2) && (@nf == 1) && (@geomtree == 0)
      s = s*sqr(@ne)
    elseif @coslimit && (@ne == 1) && \
       (@n2 == 2) && (@nf == 1) && (@geomtree == 1)
      s = 1/s + 1
    elseif !@coslimit && (@nd == 1 + @ne) && (@n == 2*@nd) &&\
       (@n2 == 2) && (@nf == 1) && (@geomtree == 1)
      s = 1/s + 1
    endif
    if (@n2 != 2) && (@n2 == 2*@nf)
      if @ne == 1
        s = 1/s + 0.5
      endif
      s = sqrt(s)
    else
      s = sqrt(sqrt(s))
    endif
  endif
  complex ssave = s

  complex ss = sqr(s)
  complex sf = 0
  if @coslimit2
    sf = cos(s)
  elseif @n2 == 3
    sf = (4*ss - 3)*s
  elseif @n2 == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n2 == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n2 == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n2 == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n2 == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n2 == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n2 == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n2 == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf

  elseif @n2 == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  if @geomtree == 1
    complex p = (u - t)/(2*rsign)
    complex a0 = t + rsign*p
    s = a0 + sf*p
  else
    complex p = (u - t)/(sf - rsign)
    complex a0 = t - rsign*p
    s = a0 - rsign*p
  endif
  complex ss = sqr(s)
  complex sf = 0

  if @coslimit
    sf = cos(s)
  elseif @n == 3
    sf = (4*ss - 3)*s
  elseif @n == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  if @geomtree == 1
    complex q = (r - ssave)/(sf + usign)
    complex a1 = ssave + usign*q
  else

    complex q = (r - ssave)/(sf + usign)
    complex a1 = ssave + usign*q
  endif
  z = u
;  z = 1
loop:
;  s = sf*z + a0
  s = z
  ss = sqr(s)
  if @coslimit
    sf = cos(s)
  elseif @n == 3
    sf = (4*ss - 3)*s
  elseif @n == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  s = sf*q + a1
  complex ss = sqr(s)
  if @coslimit2
    if abs(imag(s)) > 20
      sf = (1e10,2e10)
    else
      sf = cos(s)
    endif
  elseif @n2 == 3
    sf = (4*ss - 3)*s
  elseif @n2 == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n2 == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n2 == 6


    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n2 == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n2 == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n2 == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n2 == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n2 == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n2 == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  z = sf*p + a0
;  z = sf
bailout:
  |z| <= @bailout
default:
  title = "Chebcheb"
  center = (0, 0)
  param start

    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."
  endparam
  param n
    caption = "Order"
    default = 3
    hint = "This defines the order of the Chebyshev polynomial."
  endparam
  param n2
    caption = "Order 2"
    default = 3
    hint = "This defines the order of the 2nd Chebyshev polynomial."
  endparam
  param nd
    caption = "Destination"
    default = 1
    hint = "This defines the destination critical point."
  endparam
  param ne
    caption = "Destination 2"
    default = 2
    hint = "This defines the 2nd destination critical point."
  endparam
  param nf
    caption = "Destination 3"
    default = 1
    hint = "This defines the 3rd destination critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param coslimit
    caption = "Cosine limit"
    default = false
    hint = "As order approaches infinity we get a cosine \
            with chained critical points."
  endparam
  param coslimit2
    caption = "Cosine limit 2"
    default = false
    hint = "As order approaches infinity we get a cosine \
            with chained critical points."
  endparam
  param fold
    caption = "Fold up"
    default = false
    hint = "Fold a symmetry at 0."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 1280000.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jhebcheb"
  seed = #pixel
  power = power
  n = n
  n2 = n2
  nd = nd
  ne = ne
  nf = nf
  coslimit = coslimit
  coslimit2 = coslimit2
  geomtree = geomtree
  lowfix = lowfix
  insout = insout
  fold = fold
  bailout = bailout
}



Jhebcheb {

; Generic Julia set
init:
  complex s = @seed

  complex t = 0
  complex u = 0
  int usign = 1
  complex r = 0
  int rsign = 1
  if @coslimit
    t = #pi*@ne
  else
    complex u = cos(@nd*#pi/@n)
    if floor(0.5*@nd) == 0.5*@nd
      int usign = 1
    else
      int usign = -1
    endif
    complex t = cos(@ne*#pi/@n)
  endif
  if !@coslimit2
    complex r = cos(@nf*#pi/@n2)
    if floor(0.5*@nf) == 0.5*@nf
      int rsign = 1
    else
      int rsign = -1
    endif
  endif
  if @insout
    s = 1/s + 1
  endif
  if @fold
    if @coslimit && (floor(0.5*@ne) == 0.5*@ne) && \
       (@n2 == 2) && (@nf == 1) && (@geomtree == 0)
      s = (1/s + 1)*sqr(@ne)
    elseif @coslimit && (floor(0.5*@ne) != 0.5*@ne) && \
       (@n2 == 2) && (@nf == 1) && (@geomtree == 0)
      s = s*sqr(@ne)
    elseif @coslimit && (@ne == 1) && \
       (@n2 == 2) && (@nf == 1) && (@geomtree == 1)
      s = 1/s + 1
    elseif !@coslimit && (@nd == 1 + @ne) && (@n == 2*@nd) &&\
       (@n2 == 2) && (@nf == 1) && (@geomtree == 1)
      s = 1/s + 1
    endif
    if (@n2 != 2) && (@n2 == 2*@nf)
      if @ne == 1
        s = 1/s + 0.5
      endif
      s = sqrt(s)
    else
      s = sqrt(sqrt(s))
    endif
  endif
  complex ssave = s
  complex ss = sqr(s)
  complex sf = 0
  if @coslimit2
    sf = cos(s)
  elseif @n2 == 3
    sf = (4*ss - 3)*s
  elseif @n2 == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n2 == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n2 == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n2 == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n2 == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n2 == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n2 == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n2 == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n2 == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  if @geomtree == 1
    complex p = (u - t)/(2*rsign)

    complex a0 = t + rsign*p
    s = a0 + sf*p
  else
    complex p = (u - t)/(sf - rsign)
    complex a0 = t - rsign*p
    s = a0 - rsign*p
  endif
  complex ss = sqr(s)
  complex sf = 0
  if @coslimit
    sf = cos(s)
  elseif @n == 3
    sf = (4*ss - 3)*s
  elseif @n == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 16

    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  if @geomtree == 1
    complex q = (r - ssave)/(sf + usign)
    complex a1 = ssave + usign*q
  else
    complex q = (r - ssave)/(sf + usign)
    complex a1 = ssave + usign*q
  endif
  if @coslimit
    z = #pi*#pixel
  else
    z = #pi*#pixel
  endif
loop:
  s = z
  ss = sqr(s)
  if @coslimit
    sf = cos(s)
  elseif @n == 3
    sf = (4*ss - 3)*s
  elseif @n == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n == 9
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n == 27
    sf = (4*ss - 3)*s
    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)
  endif
  s = sf*q + a1
  complex ss = sqr(s)

  if @coslimit2
    if abs(imag(s)) > 20
      sf = (1e10,2e10)
    else
      sf = cos(s)
    endif
  elseif @n2 == 3
    sf = (4*ss - 3)*s
  elseif @n2 == 4
    sf = ((8*ss - 8)*ss + 1)
  elseif @n2 == 5
    sf = ((16*ss - 20)*ss + 5)*s
  elseif @n2 == 6
    sf = (((32*ss - 48)*ss + 18)*ss - 1)
  elseif @n2 == 7
    sf = (((64*ss - 112)*ss + 56)*ss - 7)*s
  elseif @n2 == 8
    sf = (2*sqr(2*sqr(2*ss - 1) - 1) - 1)
  elseif @n2 == 9
    sf = (4*ss - 3)*s

    sf = (4*sqr(sf) - 3)*sf
  elseif @n2 == 16
    sf = (2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1)
  elseif @n2 == 27
    sf = (4*ss - 3)*s

    sf = (4*sqr(sf) - 3)*sf
    sf = (4*sqr(sf) - 3)*sf
  elseif @n2 == 32
    sf = (2*sqr(2*sqr(2*sqr(2*sqr(2*ss - 1) - 1) - 1) - 1) - 1)
  else
    sf = (2*ss - 1)

  endif
  z = sf*p + a0
bailout:
  |z| <= @bailout
default:
  title = "Jhebcheb"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param geomtree
    caption = "Geometry"
    default = 0
    hint = "This defines the connection geometry of the critical points."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param n2
    caption = "Order 2"
    default = 3
    hint = "This defines the order of the 2nd Chebyshev polynomial."
  endparam
  param nd
    caption = "Destination"
    default = 1
    hint = "This defines the destination critical point."
  endparam
  param ne
    caption = "Destination 2"
    default = 2
    hint = "This defines the 2nd destination critical point."
  endparam
  param nf
    caption = "Destination 3"
    default = 1
    hint = "This defines the 3rd destination critical point."
  endparam
  param coslimit2
    caption = "Cosine limit 2"
    default = false
    hint = "As order approaches infinity we get a cosine \
            with chained critical points."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param lowfix
    caption = "Fix Lower"
    default = false
    hint = "Sends critical value -1 to a fixed point instead of +1."
  endparam
  param fold
    caption = "Fold up"
    default = false

    hint = "Fold a symmetry at 0."
  endparam
  param coslimit
    caption = "Cosine limit"
    default = false
    hint = "As order approaches infinity we get a cosine \
            with chained critical points."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Chebcheb"
  power = power
  bailout = bailout
}

Meet10_n_1 {
; Generic Mandelbrot set
init:
  complex s = #pixel
  if @insout
    s = 1/s + 1
  endif
  complex an5 = 1/(@n + 5)
  complex an4 = 1/(@n + 4)
  complex an3 = 1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = 1/(@n + 1)
  if @nnz == 2
    if @nn1 == 2
      complex t = (an2*s - an3*(1 + 2*s) + \
                   an4*(2 + s) - an5)/\
                  (an1*s - an2*(1 + 2*s) + \
                   an3*(2 + s) - an4)
      an4 = -an4*(2 + s + t)

      an3 = an3*(1 + 2*s + 2*t + s*t)
      an2 = -an2*(s + t + 2*s*t)
      an1 = an1*s*t
    elseif @nn1 == 1
      complex ss = sqr(s)
      complex t = (an2*ss - an3*(ss + 2*s) + \
                   an4*(1 + 2*s) - an5)/\
                  (an1*ss - an2*(ss + 2*s) + \
                   an3*(1 + 2*s) - an4)
      an4 = -an4*(1 + 2*s + t)
      an3 = an3*(2*s + t + 2*s*t + ss)
      an2 = -an2*(2*s*t + ss + ss*t)
      an1 = an1*ss*t
    else
      complex ss = sqr(s)
      complex t = (an2*ss*s - 3*an3*ss + 3*an4*s - an5)/\

                  (an1*ss*s - 3*an2*ss + 3*an3*s - an4)
      an4 = -an4*(3*s + t)
      an3 = an3*(3*s*t + 3*ss)
      an2 = -an2*(3*ss*t + ss*s)
      an1 = an1*ss*s*t
    endif
    if @swapst
      complex ss = s
      s = t
      t = ss
    endif
    complex tf = ((((an5*t + an4)*t + an3)*t + an2)*t + an1)*\
                 t^(@n + 1)
    if @swap01
      complex p = ((-s)/tf)^(1/(@n + 4))
    else
      complex p = ((1 - s)/tf)^(1/(@n + 4))
    endif
    complex pn2 = sqr(p)
    an4 = an4*p
    an3 = an3*pn2
    an2 = an2*pn2*p
    an1 = an1*pn2*pn2
  elseif @nnz == 1
    if @nn1 == 1
      complex t = (an2*s - an3*(1 + s) + an4)/\
                  (an1*s - an2*(1 + s) + an3)
      an3 = -an3*(1 + s + t)

      an2 = an2*(s*t + s + t)
      an1 = -an1*s*t
    else
      complex ss = sqr(s)
      complex t = (an2*ss - 2*an3*s + an4)/(an1*ss - 2*an2*s + an3)
      an3 = -an3*(2*s + t)
      an2 = an2*(2*s*t + ss)
      an1 = -an1*ss*t
    endif
    if @swapst
      complex ss = s
      s = t
      t = ss
    endif
    complex tt = sqr(t)
    complex tf = (an4*tt*t + an3*tt + an2*t + an1)*t^(@n + 1)
    if @swap01
      complex p = ((-s)/tf)^(1/(@n + 3))
    else
      complex p = ((1 - s)/tf)^(1/(@n + 3))
    endif
    complex pn2 = sqr(p)
    an3 = an3*p
    an2 = an2*pn2
    an1 = an1*pn2*p
  else

    complex t = (an2*s - an3)/(an1*s - an2)
    if @swapst
      ss = s
      s = t
      t = ss
    endif
    complex tf = (an3*sqr(t) - an2*(s + t)*t + an1*s*t)*t^(@n + 1)
    if @swap01
      complex p = ((-s)/tf)^an2
    else
      complex p = ((1 - s)/tf)^an2
    endif
    an2 = -an2*p*(s + t)
    an1 = an1*s*t*sqr(p)
  endif
  complex a0 = s*p
  z = a0
loop:
  if @nnz == 2
    z = ((((an5*z + an4)*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  elseif @nnz == 1
    z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  else

    z = ((an3*z + an2)*z + an1)*z^(@n + 1) + a0
  endif
bailout:
  |z| <= @bailout
default:
  title = "Meet10_n_1"

  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the zero critical point."
  endparam
  param nnz
    caption = "Order 2"
    default = 0
    hint = "This defines the excess orders of the nonzero \
            critical points."
  endparam
  param nn1
    caption = "Order 3"
    default = 0
    hint = "This defines the order of the one critical point."
  endparam
  param swapst
    caption = "Swap s t"

    default = false
    hint = "Swaps the s and t critical points"
  endparam
  param swap01
    caption = "Swap 0 1"

    default = false
    hint = "Swaps the 0 and 1 critical points"
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet10_n_1"
  seed = #pixel
  power = power
  n = n
  nnz = nnz
  nn1 = nn1
  swapst = swapst
  swap01 = swap01
  insout = insout
  bailout = bailout
}


Jeet10_n_1 {

; Generic Julia set
init:
  complex s = @seed
  if @insout
    s = 1/s + 1
  endif
  complex an5 = 1/(@n + 5)
  complex an4 = 1/(@n + 4)
  complex an3 = 1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = 1/(@n + 1)
  if @nnz == 2
    if @nn1 == 2
      complex t = (an2*s - an3*(1 + 2*s) + \
                   an4*(2 + s) - an5)/\
                  (an1*s - an2*(1 + 2*s) + \
                   an3*(2 + s) - an4)
      an4 = -an4*(2 + s + t)
      an3 = an3*(1 + 2*s + 2*t + s*t)
      an2 = -an2*(s + t + 2*s*t)
      an1 = an1*s*t
    elseif @nn1 == 1
      complex ss = sqr(s)
      complex t = (an2*ss - an3*(ss + 2*s) + \
                   an4*(1 + 2*s) - an5)/\
                  (an1*ss - an2*(ss + 2*s) + \
                   an3*(1 + 2*s) - an4)
      an4 = -an4*(1 + 2*s + t)
      an3 = an3*(2*s + t + 2*s*t + ss)
      an2 = -an2*(2*s*t + ss + ss*t)
      an1 = an1*ss*t
    else
      complex ss = sqr(s)
      complex t = (an2*ss*s - 3*an3*ss + 3*an4*s - an5)/\
                  (an1*ss*s - 3*an2*ss + 3*an3*s - an4)

      an4 = -an4*(3*s + t)
      an3 = an3*(3*s*t + 3*ss)
      an2 = -an2*(3*ss*t + ss*s)
      an1 = an1*ss*s*t
    endif
    if @swapst
      complex ss = s

      s = t
      t = ss
    endif
    complex tf = ((((an5*t + an4)*t + an3)*t + an2)*t + an1)*\
                 t^(@n + 1)
    if @swap01
      complex p = ((-s)/tf)^(1/(@n + 4))
    else
      complex p = ((1 - s)/tf)^(1/(@n + 4))
    endif
    complex pn2 = sqr(p)
    an4 = an4*p
    an3 = an3*pn2
    an2 = an2*pn2*p

    an1 = an1*pn2*pn2
  elseif @nnz == 1
    if @nn1 == 1
      complex t = (an2*s - an3*(1 + s) + an4)/\
                  (an1*s - an2*(1 + s) + an3)
      an3 = -an3*(1 + s + t)
      an2 = an2*(s*t + s + t)
      an1 = -an1*s*t
    else
      complex ss = sqr(s)

      complex t = (an2*ss - 2*an3*s + an4)/(an1*ss - 2*an2*s + an3)
      an3 = -an3*(2*s + t)
      an2 = an2*(2*s*t + ss)
      an1 = -an1*ss*t
    endif
    if @swapst
      complex ss = s
      s = t
      t = ss
    endif
    complex tt = sqr(t)

    complex tf = (an4*tt*t + an3*tt + an2*t + an1)*t^(@n + 1)
    if @swap01
      complex p = ((-s)/tf)^(1/(@n + 3))
    else
      complex p = ((1 - s)/tf)^(1/(@n + 3))
    endif
    complex pn2 = sqr(p)
    an3 = an3*p
    an2 = an2*pn2
    an1 = an1*pn2*p
  else
    complex t = (an2*s - an3)/(an1*s - an2)
    if @swapst
      ss = s
      s = t
      t = ss
    endif
    complex tf = (an3*sqr(t) - an2*(s + t)*t + an1*s*t)*t^(@n + 1)
    if @swap01
      complex p = ((-s)/tf)^an2
    else
      complex p = ((1 - s)/tf)^an2
    endif
    an2 = -an2*p*(s + t)
    an1 = an1*s*t*sqr(p)
  endif
  complex a0 = s*p
  z = 2*#pixel
loop:
  if @nnz == 2
    z = ((((an5*z + an4)*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  elseif @nnz == 1
    z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  else
    z = ((an3*z + an2)*z + an1)*z^(@n + 1) + a0
  endif
bailout:
  |z| <= @bailout
default:
  title = "Jeet10_n_1"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param nnz
    caption = "Order 2"
    default = 0
    hint = "This defines the excess orders of the nonzero \
            critical points."
  endparam
  param nn1
    caption = "Order 3"
    default = 0
    hint = "This defines the order of the one critical point."
  endparam
  param swapst
    caption = "Swap s t"
    default = false
    hint = "Swaps the s and t critical points"
  endparam
  param swap01
    caption = "Swap 0 1"
    default = false
    hint = "Swaps the 0 and 1 critical points"
  endparam
  param insout

    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet10_n_1"
  power = power
  bailout = bailout
}

Meet1_1_n_11 {
; Generic Mandelbrot set
init:
  complex s = #pixel

  if @insout
    s = 1/s
  endif
  complex brfact = @branchcut
  if @foldup == 1
    s = sqrt(s)
    complex ca2 = -1.5 + s
    complex ca1 = -1.5 - s
    complex ca0 = 1
    complex cq = (3*ca1 - ca2*ca2)/9
    complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
    if real(cr) < 0
      complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
    else
      complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
    endif
    complex wi = cq/w
    complex s = w - wi - ca2/3
    s = (s - 0.5)*0.5
    brfact = brfact*(s + 3/(16*s))
    s = s + 0.5 - 3/(16*s)
;    s = 1 - 1/s
;    s = 1 - 1/s
    brfact = brfact*(s - 1)^3
  elseif @foldup == 2
    s = sqrt(1/s + 9/16)
    brfact = brfact*(s + 3/(16*s))
    s = s + 0.5 - 3/(16*s)
    brfact = brfact*(s - 1)^3
  elseif @foldup == 5
    s = sqrt(1/(1/(1/s + 3/4) - 8/3) + 9/16)
    brfact = brfact*(s + 3/(16*s))
    s = s + 0.5 - 3/(16*s)
    brfact = brfact*(s - 1)^3
  elseif @foldup == 3
    s = 1/(sqrt(1/(s + 3/8) - 4/3) - 2/sqrt(3)) + 0.25*sqrt(3)
    brfact = brfact*(s + 3/(16*s))
    s = s + 0.5 - 3/(16*s)
    brfact = brfact*(s - 1)^3
  elseif @foldup == 4
    s = 1/(sqrt(1/(s + 1) - 0.5) - sqrt(0.5)) + sqrt(0.5)
    brfact = brfact*(s + 1/(2*s))
    s = s + 0.5 - 1/(2*s)
    brfact = brfact*(s - 1)^2
  elseif @foldup == 6
    s = 1/(sqrt(1/s - 2.25) - 1.5) + 1/3
    brfact = brfact*(s + 1/(9*s))
    s = s + 0.5 - 1/(9*s)
    brfact = brfact*(s - 1)^4
  elseif @foldup == 7
    s = sqrt(1/s - 1/9)
    brfact = brfact*(s + 1/(9*s))
    s = s + 0.5 - 1/(9*s)
    brfact = brfact*(s - 1)^4

  elseif @foldup == 8
    s = sqrt(1/s + 1/36)
    brfact = brfact*(s + 1/(9*s))
    s = s + 0.5 - 1/(9*s)
    brfact = brfact*(s - 1)^4
  else
;    brfact = brfact*(s + 3/(16*s))
;    s = s + 0.5 - 3/(16*s)
;    brfact = brfact*(s - 1)^3
  endif
  complex an6 = 1/(@n + 6)
  complex an5 = 1/(@n + 5)
  complex an4 = 1/(@n + 4)
  complex an3 = 1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = 1/(@n + 1)
  if @nnz == 3
    if @nn1 == 3
      complex ut3 = s*sqr(s)
      complex ut2 = 3*sqr(s)
      complex ut1 = 3*s
      complex ut0 = 1
    elseif @nn1 == 2
      complex ut3 = sqr(s)
      complex ut2 = 2*s + sqr(s)
      complex ut1 = 1 + 2*s
      complex ut0 = 1
    elseif @nn1 == 1
      complex ut3 = s
      complex ut2 = 1 + 2*s
      complex ut1 = 2 + s
      complex ut0 = 1
    else
      complex ut3 = 1
      complex ut2 = 3
      complex ut1 = 3
      complex ut0 = 1
    endif
    complex a1 = an4*ut3 - an3*ut2 + an2*ut1 - an1*ut0
    complex b1 = (an5*ut3 - an4*ut2 + an3*ut1 - an2*ut0)*s
    complex c1 = (an6*ut3 - an5*ut2 + an4*ut1 - an3*ut0)*sqr(s)
    if @nn1 == 3
      complex ut3 = 1

      complex ut2 = 3
      complex ut1 = 3
      complex ut0 = 1
    elseif @nn1 == 2
      complex ut3 = 1
      complex ut2 = 2 + s
      complex ut1 = 1 + 2*s
      complex ut0 = s
    elseif @nn1 == 1
      complex ut3 = 1
      complex ut2 = 1 + 2*s
      complex ut1 = 2*s + sqr(s)
      complex ut0 = sqr(s)
    else
      complex ut3 = 1
      complex ut2 = 3*s
      complex ut1 = 3*sqr(s)
      complex ut0 = s*sqr(s)
    endif
    complex a0 = an4*ut3 - an3*ut2 + an2*ut1 - an1*ut0
    complex b0 = an5*ut3 - an4*ut2 + an3*ut1 - an2*ut0
    complex c0 = an6*ut3 - an5*ut2 + an4*ut1 - an3*ut0
  elseif @nnz == 2
    if @nn1 == 2
      complex ut2 = sqr(s)
      complex ut1 = 2*s
      complex ut0 = 1
    elseif @nn1 == 1
      complex ut2 = s
      complex ut1 = 1 + s
      complex ut0 = 1
    else
      complex ut2 = 1
      complex ut1 = 2
      complex ut0 = 1
    endif
    complex a1 = an3*ut2 - an2*ut1 + an1*ut0
    complex b1 = (an4*ut2 - an3*ut1 + an2*ut0)*s
    complex c1 = (an5*ut2 - an4*ut1 + an3*ut0)*sqr(s)
    if @nn1 == 2
      complex ut2 = 1
      complex ut1 = 2
      complex ut0 = 1
    elseif @nn1 == 1
      complex ut2 = 1
      complex ut1 = 1 + s
      complex ut0 = s
    else
      complex ut2 = 1
      complex ut1 = 2*s
      complex ut0 = sqr(s)
    endif
    complex a0 = an3*ut2 - an2*ut1 + an1*ut0
    complex b0 = an4*ut2 - an3*ut1 + an2*ut0
    complex c0 = an5*ut2 - an4*ut1 + an3*ut0
  elseif @nnz == 1
    if @nn1 == 1
      complex ut1 = s
      complex ut0 = 1
    else
      complex ut1 = 1
      complex ut0 = 1
    endif
    complex a1 = an2*ut1 - an1*ut0
    complex b1 = (an3*ut1 - an2*ut0)*s
    complex c1 = (an4*ut1 - an3*ut0)*sqr(s)
    if @nn1 == 1
      complex ut1 = 1
      complex ut0 = 1
    else
      complex ut1 = 1
      complex ut0 = s
    endif
    complex a0 = an2*ut1 - an1*ut0
    complex b0 = an3*ut1 - an2*ut0
    complex c0 = an4*ut1 - an3*ut0
  else
    complex ut0 = 1
    complex a1 = an2*ut1 - an1*ut0
    complex b1 = (an3*ut1 - an2*ut0)*s
    complex c1 = (an4*ut1 - an3*ut0)*sqr(s)
    complex ut0 = 1
    complex a0 = an2*ut1 - an1*ut0
    complex b0 = an3*ut1 - an2*ut0
    complex c0 = an4*ut1 - an3*ut0
  endif
  complex qa = a0*b1 - a1*b0
  complex qb = a0*c1 - a1*c0
  complex qc = b0*c1 - b1*c0
  complex qrad = sqrt((sqr(qb) - 4*qa*qc)/sqr(brfact))
  complex iqa = 1/(2*qa)
  complex t = (qb + qrad*brfact)*iqa
  complex u = (qb - qrad*brfact)*iqa
  complex ut = u*t
  complex upt = u + t
  if @nnz == 3
    an5 = -an5*(upt + ut2)
    an4 = an4*(ut + upt*ut2 + ut1)
    an3 = -an3*(ut*ut2 + upt*ut1 + ut0)
    an2 = an2*(ut*ut1 + upt*ut0)
    an1 = -an1*ut*ut0
  elseif @nnz == 2
    an4 = -an4*(upt + ut1)
    an3 = an3*(ut + upt*ut1 + ut0)
    an2 = -an2*(ut*ut1 + upt*ut0)
    an1 = an1*ut*ut0

  elseif @nnz == 1
    an3 = -an3*(upt + ut0)
    an2 = an2*(ut + upt*ut0)
    an1 = -an1*ut*ut0
  else
    an2 = -an2*upt
    an1 = an1*ut
  endif
  if @nnz == 3
    complex tf = (((((an6*t + an5)*t + an4)*t + an3)*t + an2)\
                  *t + an1)*t^(@n + 1)
    complex uf = (((((an6*u + an5)*u + an4)*u + an3)*u + an2)\
                  *u + an1)*u^(@n + 1)
  elseif @nnz == 2
    complex tf = ((((an5*t + an4)*t + an3)*t + an2)\
                  *t + an1)*t^(@n + 1)
    complex uf = ((((an5*u + an4)*u + an3)*u + an2)\
                  *u + an1)*u^(@n + 1)
  elseif @nnz == 1
    complex tf = (((an4*t + an3)*t + an2)\
                  *t + an1)*t^(@n + 1)
    complex uf = (((an4*u + an3)*u + an2)\
                  *u + an1)*u^(@n + 1)
  else
    complex tf = ((an3*t + an2)\
                  *t + an1)*t^(@n + 1)
    complex uf = ((an3*u + an2)\
                  *u + an1)*u^(@n + 1)
  endif
  if @geomtree == 3
    complex pn1z = (u - s)/(tf - uf)
    complex a0 = s - uf*pn1z
  elseif @geomtree == 2
    complex pn1z = 1/(tf - uf)
    complex a0 = -uf*pn1z
  elseif @geomtree == 1
    complex pn1z = (s - t)/uf
    complex a0 = t
  else
    complex pn1z = (u - t)/tf
    complex a0 = t
  endif
  if @nnz == 3
    complex p = pn1z^(1/(@n + 5))
    complex pn2 = sqr(p)
    an5 = an5*p
    an4 = an4*pn2
    an3 = an3*pn2*p
    an2 = an2*pn2*pn2
    an1 = an1*pn2*pn2*p
  elseif @nnz == 2
    complex p = pn1z^(1/(@n + 4))
    complex pn2 = sqr(p)
    an4 = an4*p
    an3 = an3*pn2
    an2 = an2*pn2*p
    an1 = an1*pn2*pn2
  elseif @nnz == 1
    complex p = pn1z^(1/(@n + 3))
    complex pn2 = sqr(p)
    an3 = an3*p
    an2 = an2*pn2
    an1 = an1*pn2*p
  else
    complex p = pn1z^(1/(@n + 2))
    complex pn2 = sqr(p)
    an2 = an2*p
    an1 = an1*pn2
  endif
  a0 = a0*p
  z = a0
  if @showbranch && (10*real(qrad) < abs(imag(qrad)))
    z = 1e15
  endif
loop:
  if @nnz == 3
    z = (((((an6*z + an5)*z + an4)*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  elseif @nnz == 2
    z = ((((an5*z + an4)*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0

  elseif @nnz == 1
    z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  else
    z = ((an3*z + an2)*z + an1)*z^(@n + 1) + a0
  endif
bailout:
  |z| <= @bailout
default:
  title = "Meet1_1_n_11"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)

    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param geomtree
    caption = "Geometry"
    default = 2
    hint = "This sets various critical point interconnections."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the zero critical point."
  endparam
  param nnz
    caption = "Order 2"
    default = 2
    hint = "This defines the excess orders of the nonzero \
            critical points."
  endparam
  param nn1
    caption = "Order 3"
    default = 1
    hint = "This defines the order of the one critical point."
  endparam
  param foldup
    caption = "Fold Up"
    default = 3
    hint = "This folds up symmetries in various ways."
  endparam
  param swapst
    caption = "Swap s t"
    default = false
    hint = "Swaps the s and t critical points"
  endparam
  param swap01
    caption = "Swap 0 1"
    default = false
    hint = "Swaps the 0 and 1 critical points"
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,1)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param showbranch
    caption = "Show branches"
    default = false
    hint = "There are six branch points to this parametization. This \

            unwraps two and duplicates the rest."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet1_1_n_11"
  seed = #pixel
  power = power
  foldup = foldup
  geomtree = geomtree
  branchcut = branchcut
  n = n
  nnz = nnz
  nn1 = nn1
  swapst = swapst

  swap01 = swap01
  insout = insout
  bailout = bailout
}


Jeet1_1_n_11 {

; Generic Julia set
init:
  complex s = @seed
  if @insout
    s = 1/s
  endif
  complex brfact = @branchcut
  if @foldup == 1
    s = sqrt(s)
    complex ca2 = -1.5 + s
    complex ca1 = -1.5 - s
    complex ca0 = 1
    complex cq = (3*ca1 - ca2*ca2)/9
    complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
    if real(cr) < 0
      complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
    else
      complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
    endif
    complex wi = cq/w
    complex s = w - wi - ca2/3
    s = (s - 0.5)*0.5
    brfact = brfact*(s + 3/(16*s))
    s = s + 0.5 - 3/(16*s)
;    s = 1 - 1/s
;    s = 1 - 1/s
    brfact = brfact*(s - 1)^3
  elseif @foldup == 2
    s = sqrt(1/s + 9/16)
    brfact = brfact*(s + 3/(16*s))
    s = s + 0.5 - 3/(16*s)
    brfact = brfact*(s - 1)^3
  elseif @foldup == 5
    s = sqrt(1/(1/(1/s + 3/4) - 8/3) + 9/16)
    brfact = brfact*(s + 3/(16*s))
    s = s + 0.5 - 3/(16*s)
    brfact = brfact*(s - 1)^3
  elseif @foldup == 3
    s = 1/(sqrt(1/(s + 3/8) - 4/3) - 2/sqrt(3)) + 0.25*sqrt(3)
    brfact = brfact*(s + 3/(16*s))
    s = s + 0.5 - 3/(16*s)
    brfact = brfact*(s - 1)^3
  elseif @foldup == 4
    s = 1/(sqrt(1/(s + 1) - 0.5) - sqrt(0.5)) + sqrt(0.5)
    brfact = brfact*(s + 1/(2*s))
    s = s + 0.5 - 1/(2*s)
    brfact = brfact*(s - 1)^2
  elseif @foldup == 6
    s = 1/(sqrt(1/s - 2.25) - 1.5) + 1/3
    brfact = brfact*(s + 1/(9*s))
    s = s + 0.5 - 1/(9*s)
    brfact = brfact*(s - 1)^4
  elseif @foldup == 7
    s = sqrt(1/s - 1/9)
    brfact = brfact*(s + 1/(9*s))
    s = s + 0.5 - 1/(9*s)
    brfact = brfact*(s - 1)^4
  elseif @foldup == 8
    s = sqrt(1/s + 1/36)
    brfact = brfact*(s + 1/(9*s))
    s = s + 0.5 - 1/(9*s)
    brfact = brfact*(s - 1)^4
  else
;    brfact = brfact*(s + 3/(16*s))
;    s = s + 0.5 - 3/(16*s)
;    brfact = brfact*(s - 1)^3
  endif
  complex an6 = 1/(@n + 6)
  complex an5 = 1/(@n + 5)
  complex an4 = 1/(@n + 4)
  complex an3 = 1/(@n + 3)
  complex an2 = 1/(@n + 2)
  complex an1 = 1/(@n + 1)
  if @nnz == 3
    if @nn1 == 3
      complex ut3 = s*sqr(s)
      complex ut2 = 3*sqr(s)
      complex ut1 = 3*s
      complex ut0 = 1
    elseif @nn1 == 2
      complex ut3 = sqr(s)
      complex ut2 = 2*s + sqr(s)
      complex ut1 = 1 + 2*s
      complex ut0 = 1
    elseif @nn1 == 1
      complex ut3 = s
      complex ut2 = 1 + 2*s
      complex ut1 = 2 + s
      complex ut0 = 1
    else
      complex ut3 = 1
      complex ut2 = 3
      complex ut1 = 3
      complex ut0 = 1
    endif
    complex a1 = an4*ut3 - an3*ut2 + an2*ut1 - an1*ut0
    complex b1 = (an5*ut3 - an4*ut2 + an3*ut1 - an2*ut0)*s
    complex c1 = (an6*ut3 - an5*ut2 + an4*ut1 - an3*ut0)*sqr(s)
    if @nn1 == 3
      complex ut3 = 1
      complex ut2 = 3
      complex ut1 = 3
      complex ut0 = 1
    elseif @nn1 == 2
      complex ut3 = 1
      complex ut2 = 2 + s
      complex ut1 = 1 + 2*s
      complex ut0 = s
    elseif @nn1 == 1
      complex ut3 = 1
      complex ut2 = 1 + 2*s
      complex ut1 = 2*s + sqr(s)
      complex ut0 = sqr(s)
    else
      complex ut3 = 1
      complex ut2 = 3*s
      complex ut1 = 3*sqr(s)
      complex ut0 = s*sqr(s)
    endif
    complex a0 = an4*ut3 - an3*ut2 + an2*ut1 - an1*ut0
    complex b0 = an5*ut3 - an4*ut2 + an3*ut1 - an2*ut0
    complex c0 = an6*ut3 - an5*ut2 + an4*ut1 - an3*ut0

  elseif @nnz == 2
    if @nn1 == 2
      complex ut2 = sqr(s)
      complex ut1 = 2*s
      complex ut0 = 1
    elseif @nn1 == 1
      complex ut2 = s
      complex ut1 = 1 + s
      complex ut0 = 1
    else
      complex ut2 = 1
      complex ut1 = 2
      complex ut0 = 1
    endif
    complex a1 = an3*ut2 - an2*ut1 + an1*ut0
    complex b1 = (an4*ut2 - an3*ut1 + an2*ut0)*s
    complex c1 = (an5*ut2 - an4*ut1 + an3*ut0)*sqr(s)
    if @nn1 == 2

      complex ut2 = 1
      complex ut1 = 2
      complex ut0 = 1
    elseif @nn1 == 1
      complex ut2 = 1
      complex ut1 = 1 + s
      complex ut0 = s
    else
      complex ut2 = 1
      complex ut1 = 2*s
      complex ut0 = sqr(s)
    endif
    complex a0 = an3*ut2 - an2*ut1 + an1*ut0
    complex b0 = an4*ut2 - an3*ut1 + an2*ut0
    complex c0 = an5*ut2 - an4*ut1 + an3*ut0
  elseif @nnz == 1
    if @nn1 == 1
      complex ut1 = s
      complex ut0 = 1
    else
      complex ut1 = 1
      complex ut0 = 1

    endif
    complex a1 = an2*ut1 - an1*ut0
    complex b1 = (an3*ut1 - an2*ut0)*s
    complex c1 = (an4*ut1 - an3*ut0)*sqr(s)
    if @nn1 == 1
      complex ut1 = 1
      complex ut0 = 1
    else
      complex ut1 = 1
      complex ut0 = s
    endif
    complex a0 = an2*ut1 - an1*ut0
    complex b0 = an3*ut1 - an2*ut0
    complex c0 = an4*ut1 - an3*ut0
  else
    complex ut0 = 1
    complex a1 = an2*ut1 - an1*ut0

    complex b1 = (an3*ut1 - an2*ut0)*s
    complex c1 = (an4*ut1 - an3*ut0)*sqr(s)
    complex ut0 = 1

    complex a0 = an2*ut1 - an1*ut0
    complex b0 = an3*ut1 - an2*ut0
    complex c0 = an4*ut1 - an3*ut0
  endif
  complex qa = a0*b1 - a1*b0
  complex qb = a0*c1 - a1*c0
  complex qc = b0*c1 - b1*c0
  complex qrad = sqrt((sqr(qb) - 4*qa*qc)/sqr(brfact))
  complex iqa = 1/(2*qa)
  complex t = (qb + qrad*brfact)*iqa
  complex u = (qb - qrad*brfact)*iqa
  complex ut = u*t
  complex upt = u + t
  if @nnz == 3
    an5 = -an5*(upt + ut2)
    an4 = an4*(ut + upt*ut2 + ut1)
    an3 = -an3*(ut*ut2 + upt*ut1 + ut0)
    an2 = an2*(ut*ut1 + upt*ut0)
    an1 = -an1*ut*ut0
  elseif @nnz == 2

    an4 = -an4*(upt + ut1)
    an3 = an3*(ut + upt*ut1 + ut0)
    an2 = -an2*(ut*ut1 + upt*ut0)
    an1 = an1*ut*ut0
  elseif @nnz == 1
    an3 = -an3*(upt + ut0)
    an2 = an2*(ut + upt*ut0)
    an1 = -an1*ut*ut0
  else
    an2 = -an2*upt
    an1 = an1*ut
  endif
  if @nnz == 3
    complex tf = (((((an6*t + an5)*t + an4)*t + an3)*t + an2)\
                  *t + an1)*t^(@n + 1)
    complex uf = (((((an6*u + an5)*u + an4)*u + an3)*u + an2)\
                  *u + an1)*u^(@n + 1)
  elseif @nnz == 2
    complex tf = ((((an5*t + an4)*t + an3)*t + an2)\
                  *t + an1)*t^(@n + 1)
    complex uf = ((((an5*u + an4)*u + an3)*u + an2)\
                  *u + an1)*u^(@n + 1)
  elseif @nnz == 1
    complex tf = (((an4*t + an3)*t + an2)\
                  *t + an1)*t^(@n + 1)
    complex uf = (((an4*u + an3)*u + an2)\
                  *u + an1)*u^(@n + 1)

  else
    complex tf = ((an3*t + an2)\
                  *t + an1)*t^(@n + 1)
    complex uf = ((an3*u + an2)\
                  *u + an1)*u^(@n + 1)
  endif
  if @geomtree == 3
    complex pn1z = (u - s)/(tf - uf)
    complex a0 = s - uf*pn1z
  elseif @geomtree == 2
    complex pn1z = 1/(tf - uf)
    complex a0 = -uf*pn1z
  elseif @geomtree == 1
    complex pn1z = (s - t)/uf
    complex a0 = t
  else
    complex pn1z = (u - t)/tf
    complex a0 = t
  endif
  if @nnz == 3
    complex p = pn1z^(1/(@n + 5))
    complex pn2 = sqr(p)
    an5 = an5*p
    an4 = an4*pn2
    an3 = an3*pn2*p
    an2 = an2*pn2*pn2
    an1 = an1*pn2*pn2*p
  elseif @nnz == 2
    complex p = pn1z^(1/(@n + 4))
    complex pn2 = sqr(p)
    an4 = an4*p
    an3 = an3*pn2
    an2 = an2*pn2*p
    an1 = an1*pn2*pn2

  elseif @nnz == 1
    complex p = pn1z^(1/(@n + 3))
    complex pn2 = sqr(p)
    an3 = an3*p
    an2 = an2*pn2
    an1 = an1*pn2*p
  else
    complex p = pn1z^(1/(@n + 2))
    complex pn2 = sqr(p)
    an2 = an2*p
    an1 = an1*pn2
  endif
  a0 = a0*p
  z = 2*#pixel
loop:
  if @nnz == 3
    z = (((((an6*z + an5)*z + an4)*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  elseif @nnz == 2
    z = ((((an5*z + an4)*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  elseif @nnz == 1
    z = (((an4*z + an3)*z + an2)*z + an1)*z^(@n + 1) + a0
  else

    z = ((an3*z + an2)*z + an1)*z^(@n + 1) + a0
  endif
bailout:
  |z| <= @bailout
default:
  title = "Jeet1_1_n_11"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param geomtree
    caption = "Geometry"
    default = 1
    hint = "This sets various critical point interconnections."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the zero critical point."
  endparam
  param nnz
    caption = "Order 2"
    default = 2
    hint = "This defines the excess orders of the nonzero \
            critical points."
  endparam
  param nn1
    caption = "Order 3"
    default = 1
    hint = "This defines the order of the one critical point."
  endparam
  param foldup
    caption = "Fold Up"
    default = 2
    hint = "This folds up symmetries in various ways."
  endparam
  param swapst
    caption = "Swap s t"
    default = false
    hint = "Swaps the s and t critical points"
  endparam
  param swap01
    caption = "Swap 0 1"
    default = false
    hint = "Swaps the 0 and 1 critical points"
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."

  endparam

  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0

    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet1_1_n_11"
  power = power
  bailout = bailout
}

Meet11_11_0 {
; Generic Mandelbrot set
init:
  complex st = #pixel

  if @insout
    st = 1/st
  endif
  complex sqst = sqrt(sqr(st) - 0.2)
  complex s = sqst + st
  complex t = sqst - st
  complex a5 = 0.2
  complex a4 = -0.25*(s + t)
  complex a3 = -0.4
  complex a2 = 0.5*(s + t)
  complex a1 = 0.2
  complex q = ((((a5*s + a4)*s + a3)*s + a2)*s + a1)*s
  complex r = ((((a5*t + a4)*t + a3)*t + a2)*t + a1)*t
  complex pn4 = 2/(q - r)
  complex u = 1 - q*pn4
  complex pn2 = sqrt(pn4)
  complex p = sqrt(pn2)
  a4 = a4*p
  a3 = a3*pn2
  a2 = a2*pn2*p
  a1 = a1*pn4
  complex a0 = u*p
  z = p
loop:
  z = ((((a5*z + a4)*z + a3)*z + a2)*z + a1)*z + a0
bailout:
  |z| <= @bailout
default:

  title = "Meet11_11_0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet11_11_0"
  seed = #pixel
  power = power
  n = n
  insout = insout
  bailout = bailout
}


Jeet11_11_0 {

; Generic Julia set
init:
  complex st = @seed
  if @insout
    st = 1/st
  endif
  complex sqst = sqrt(sqr(st) - 0.2)
  complex s = sqst + st
  complex t = sqst - st
  complex a5 = 0.2
  complex a4 = -0.25*(s + t)
  complex a3 = -0.4
  complex a2 = 0.5*(s + t)
  complex a1 = 0.2
  complex q = ((((a5*s + a4)*s + a3)*s + a2)*s + a1)*s
  complex r = ((((a5*t + a4)*t + a3)*t + a2)*t + a1)*t
  complex pn4 = 2/(q - r)
  complex u = 1 - q*pn4
  complex pn2 = sqrt(pn4)
  complex p = sqrt(pn2)
  a4 = a4*p
  a3 = a3*pn2
  a2 = a2*pn2*p
  a1 = a1*pn4
  complex a0 = u*p
  z = 2*#pixel

loop:

  z = ((((a5*z + a4)*z + a3)*z + a2)*z + a1)*z + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet11_11_0"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param n
    caption = "Order"
    default = 1

    hint = "This defines the order of the fourth critical point."

  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet11_11_0"
  power = power
  bailout = bailout
}

Meet12_12_0 {
; Generic Mandelbrot set
init:
  complex st = #pixel
  if @insout
    st = 1/st
  endif
  complex a7 = 1/7
  complex sqst = sqrt(sqr(st) - a7)
  complex s = sqst + st
  complex t = sqst - st
  complex a6 = -(s + t)/6
  complex a5 = -3*a7
  complex a4 = 0.5*(s + t)
  complex a3 = -a5
  complex a2 = -a4
  complex a1 = -a7
  complex q = ((((((a7*s + a6)*s + a5)*s + a4)*s + a3)*s + a2)*s + a1)*s
  complex r = ((((((a7*t + a6)*t + a5)*t + a4)*t + a3)*t + a2)*t + a1)*t
  complex pn6 = 2/(q - r)
  complex u = 1 - q*pn6
  complex p = pn6^(1/6)
  complex pn2 = sqr(p)

  a6 = a6*p
  a5 = a5*pn2
  a4 = a4*pn2*p
  a3 = a3*pn2*pn2
  a2 = a2*pn2*pn2*p
  a1 = a1*pn6
  complex a0 = u*p
  z = p
loop:
  z = ((((((a7*z + a6)*z + a5)*z + a4)*z + a3)*z + a2)*z + a1)*z + a0
bailout:
  |z| <= @bailout
default:
  title = "Meet12_12_0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0

    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet12_12_0"
  seed = #pixel
  power = power
  n = n
  insout = insout
  bailout = bailout
}


Jeet12_12_0 {

; Generic Julia set
init:
  complex st = @seed
  if @insout
    st = 1/st
  endif
  complex a7 = 1/7

  complex sqst = sqrt(sqr(st) - a7)
  complex s = sqst + st
  complex t = sqst - st
  complex a6 = -(s + t)/6
  complex a5 = -3*a7
  complex a4 = 0.5*(s + t)
  complex a3 = -a5
  complex a2 = -a4
  complex a1 = -a7
  complex q = ((((((a7*s + a6)*s + a5)*s + a4)*s + a3)*s + a2)*s + a1)*s
  complex r = ((((((a7*t + a6)*t + a5)*t + a4)*t + a3)*t + a2)*t + a1)*t
  complex pn6 = 2/(q - r)
  complex u = 1 - q*pn6
  complex p = pn6^(1/6)
  complex pn2 = sqr(p)
  a6 = a6*p
  a5 = a5*pn2
  a4 = a4*pn2*p
  a3 = a3*pn2*pn2
  a2 = a2*pn2*pn2*p

  a1 = a1*pn6
  complex a0 = u*p
  z = 2*#pixel

loop:
  z = ((((((a7*z + a6)*z + a5)*z + a4)*z + a3)*z + a2)*z + a1)*z + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet12_12_0"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param n
    caption = "Order"
    default = 1

    hint = "This defines the order of the fourth critical point."
  endparam
  param insout
    caption = "Inside Out"
    default = false
    hint = "Remaps infinity to a pole."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."

  endparam
switch:
  type = "Meet12_12_0"
  power = power
  bailout = bailout
}

Meet1000_1_0 {
; Generic Mandelbrot set
init:
  complex t = #pixel
  complex tb = t*@branchcut
  complex m = (2*t - 3)*sqr(t)

  complex d = 0.5*((t - 0.75)*m + t - 1.5)
  complex ca2 = -1.125
  complex ca1 = -d
  complex ca0 = -sqr(m)*0.03125
  complex cq = (3*ca1 - ca2*ca2)/9
  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
  if real(cr) < 0
    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  endif
  complex wi = cq/w
  complex k = w - wi - ca2/3
  complex sq2k = sqrt(2*k)
  complex mok = m/(4*sq2k)
  complex qrad = sqrt(2*k - 4*(mok - 0.5625 + k))
  complex u0 = 0.5*(-sq2k + qrad) + 0.75
  complex u1 = 0.5*(-sq2k - qrad) + 0.75
  complex qrad = sqrt(2*k - 4*(-mok - 0.5625 + k))
  complex u2 = 0.5*(sq2k + qrad) + 0.75
  complex u3 = 0.5*(sq2k - qrad) + 0.75
  complex u = 0
  if |tb - u0| > |tb - u1|
    u = u0
    u0 = u1
    u1 = u
  endif
  if |tb - u2| > |tb - u3|
    u = u2
    u2 = u3
    u3 = u
  endif
  if |tb - u0| > |tb - u2|
    u = u0
    u0 = u2
    u2 = u
  endif
  if |tb - u1| > |tb - u3|
    u = u1
    u1 = u3
    u3 = u
  endif
  if |tb - u1| > |tb - u2|
    u = u1
    u1 = u2
    u2 = u
  endif
  if @sheet == 0
    u = u0
  elseif @sheet == 1
    u = u1
  elseif @sheet == 2
    u = u2
  elseif @sheet == 3
    u = u3
  elseif @sheet == 4
    u = u0
    if imag(tb) > 0
      u = u1
    endif

  elseif @sheet == 5
    u = u1
    if imag(tb) > 0
      u = u2
    endif
  else
    u = u2
    if imag(tb) > 0
      u = u3
    endif
  endif
  complex s = (m*u + 1.5)/(m + 1)
  complex p = sqrt(6*(s - u))
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*p
  complex a0 = s*p
  z = a0
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Meet1000_1_0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param sheet
    caption = "Sheets"
    default = 0
    hint = "This has three sheets.  Choose bottom, middle, top, half \
            bottom half mid, or half mid half top."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet1000_1_0"
  seed = #pixel
  power = power
  sheet = sheet
  branchcut = branchcut
  bailout = bailout
}


Jeet1000_1_0 {

; Generic Julia set
init:

  complex t = @seed
  complex tb = t*@branchcut
  complex m = (2*t - 3)*sqr(t)
  complex d = 0.5*((t - 0.75)*m + t - 1.5)
  complex ca2 = -1.125
  complex ca1 = -d
  complex ca0 = -sqr(m)*0.03125
  complex cq = (3*ca1 - ca2*ca2)/9
  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54

  if real(cr) < 0
    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  endif
  complex wi = cq/w
  complex k = w - wi - ca2/3
  complex sq2k = sqrt(2*k)
  complex mok = m/(4*sq2k)

  complex qrad = sqrt(2*k - 4*(mok - 0.5625 + k))
  complex u0 = 0.5*(-sq2k + qrad) + 0.75
  complex u1 = 0.5*(-sq2k - qrad) + 0.75
  complex qrad = sqrt(2*k - 4*(-mok - 0.5625 + k))
  complex u2 = 0.5*(sq2k + qrad) + 0.75
  complex u3 = 0.5*(sq2k - qrad) + 0.75
  complex u = 0
  if |tb - u0| > |tb - u1|
    u = u0
    u0 = u1
    u1 = u
  endif
  if |tb - u2| > |tb - u3|
    u = u2
    u2 = u3
    u3 = u
  endif
  if |tb - u0| > |tb - u2|
    u = u0
    u0 = u2
    u2 = u
  endif
  if |tb - u1| > |tb - u3|
    u = u1
    u1 = u3
    u3 = u
  endif
  if |tb - u1| > |tb - u2|
    u = u1
    u1 = u2
    u2 = u
  endif
  if @sheet == 0
    u = u0
  elseif @sheet == 1
    u = u1
  elseif @sheet == 2
    u = u2
  elseif @sheet == 3
    u = u3
  elseif @sheet == 4
    u = u0
    if imag(tb) > 0
      u = u1
    endif
  elseif @sheet == 5
    u = u1
    if imag(tb) > 0
      u = u2
    endif
  else
    u = u2
    if imag(tb) > 0
      u = u3
    endif
  endif
  complex s = (m*u + 1.5)/(m + 1)
  complex p = sqrt(6*(s - u))
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*p
  complex a0 = s*p
  z = #pixel*2
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet1000_1_0"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param sheet
    caption = "Sheets"
    default = 0

    hint = "This has three sheets.  Choose bottom, middle, top, half \
            bottom half mid, or half mid half top."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."

  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet1000_1_0"
  power = power
  bailout = bailout
}

Meet100_n_1 {
; Generic Mandelbrot set
init:
  complex u = #pixel
  complex ub = u*@branchcut
  float n1 = @n + 1
  float n2 = @n + 2
  float n3 = @n + 3
  complex un1 = u^n1
  complex uu = sqr(u)
  complex b2 = n2 - n1*u
  complex b1 = n1*uu - n3
  complex b0 = n3*u - n2*uu
  complex c2 = n1*n2
  complex c1 = -(u + 1)*n1*n3
  complex c0 = n2*n3*u
  complex ia4 = 1/(un1*b2*c2 + n1)
  complex a3 = 0.25*(un1*(b2*c1 + b1*c2) - 2*n1 - n3)*ia4
  complex a2 = (un1*(b2*c0 + b1*c1 + b0*c2) + n1 + 2*n3)*ia4
  complex a1 = (un1*(b1*c0 + b0*c1) - n3)*ia4
  complex a0 = un1*b0*c0*ia4
  a3a3 = sqr(a3)
  a0 = a0 - a1*a3 + a2*a3a3 - 3*sqr(a3a3)
  a1 = a1 - 2*a2*a3 + 8*a3a3*a3
  a2 = a2 - 6*a3a3
  complex ca2 = -0.5*a2
  complex ca1 = -a0
  complex ca0 = 0.5*a0*a2 - 0.125*sqr(a1)
  complex cq = (3*ca1 - ca2*ca2)/9
  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
  if real(cr) < 0

    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  endif
  complex wi = cq/w
  complex k = w - wi - ca2/3
  complex sq2k = sqrt(2*k - a2)
  complex mok = -0.5*a1/sq2k
  complex qrad = sqrt(sqr(sq2k) - 4*(k + mok))
  complex t0 = 0.5*(-sq2k + qrad) - a3
  complex t1 = 0.5*(-sq2k - qrad) - a3
  complex qrad = sqrt(sqr(sq2k) - 4*(k - mok))
  complex t2 = 0.5*(sq2k + qrad) - a3
  complex t3 = 0.5*(sq2k - qrad) - a3
  complex t = 0
  if |ub - t0| > |ub - t1|
    t = t0
    t0 = t1
    t1 = t
  endif
  if |ub - t2| > |ub - t3|
    t = t2
    t2 = t3

    t3 = t
  endif
  if |ub - t0| > |ub - t2|
    t = t0
    t0 = t2
    t2 = t
  endif
  if |ub - t1| > |ub - t3|
    t = t1
    t1 = t3
    t3 = t
  endif
  if |ub - t1| > |ub - t2|
    t = t1
    t1 = t2
    t2 = t
  endif
  if @sheet == 0
    t = t0
  elseif @sheet == 1
    t = t1
  elseif @sheet == 2
    t = t2
  elseif @sheet == 3
    t = t3
  elseif @sheet == 4
    t = t0
    if imag(ub) > 0
      t = t1
    endif
  elseif @sheet == 5
    t = t1
    if imag(ub) > 0
      t = t2
    endif
  else
    t = t2
    if imag(ub) > 0
      t = t3
    endif
  endif
  complex an3 = 1/n3

  complex an2 = 1/n2
  complex an1 = 1/n1
  complex s = (an3*t*t - an2*t)/(an2*t - an1)
  complex p = ((u - s)/(an3 - (1 + s)*an2 + s*an1))^an2
  complex an2 = -an2*(1 + s)*p
  complex an1 = an1*s*p*p
  complex a0 = s*p
  z = a0
loop:
  z = ((an3*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Meet100_n_1"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param sheet
    caption = "Sheets"
    default = 0
    hint = "This has three sheets.  Choose bottom, middle, top, half \
            bottom half mid, or half mid half top."

  endparam
  param n

    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."

  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeet100_n_1"
  seed = #pixel
  power = power
  n = n
  sheet = sheet
  branchcut = branchcut
  bailout = bailout
}


Jeet100_n_1 {

; Generic Julia set
init:
  complex u = @seed
  complex ub = u*@branchcut
  float n1 = @n + 1
  float n2 = @n + 2
  float n3 = @n + 3
  complex un1 = u^n1
  complex uu = sqr(u)

  complex b2 = n2 - n1*u
  complex b1 = n1*uu - n3
  complex b0 = n3*u - n2*uu
  complex c2 = n1*n2
  complex c1 = -(u + 1)*n1*n3
  complex c0 = n2*n3*u
  complex ia4 = 1/(un1*b2*c2 + n1)
  complex a3 = 0.25*(un1*(b2*c1 + b1*c2) - 2*n1 - n3)*ia4
  complex a2 = (un1*(b2*c0 + b1*c1 + b0*c2) + n1 + 2*n3)*ia4
  complex a1 = (un1*(b1*c0 + b0*c1) - n3)*ia4
  complex a0 = un1*b0*c0*ia4
  a3a3 = sqr(a3)
  a0 = a0 - a1*a3 + a2*a3a3 - 3*sqr(a3a3)
  a1 = a1 - 2*a2*a3 + 8*a3a3*a3
  a2 = a2 - 6*a3a3
  complex ca2 = -0.5*a2
  complex ca1 = -a0
  complex ca0 = 0.5*a0*a2 - 0.125*sqr(a1)
  complex cq = (3*ca1 - ca2*ca2)/9

  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
  if real(cr) < 0
    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  endif
  complex wi = cq/w
  complex k = w - wi - ca2/3
  complex sq2k = sqrt(2*k - a2)
  complex mok = -0.5*a1/sq2k
  complex qrad = sqrt(sqr(sq2k) - 4*(k + mok))
  complex t0 = 0.5*(-sq2k + qrad) - a3
  complex t1 = 0.5*(-sq2k - qrad) - a3
  complex qrad = sqrt(sqr(sq2k) - 4*(k - mok))

  complex t2 = 0.5*(sq2k + qrad) - a3
  complex t3 = 0.5*(sq2k - qrad) - a3
  complex t = 0
  if |ub - t0| > |ub - t1|
    t = t0
    t0 = t1
    t1 = t
  endif
  if |ub - t2| > |ub - t3|
    t = t2
    t2 = t3
    t3 = t
  endif
  if |ub - t0| > |ub - t2|
    t = t0
    t0 = t2
    t2 = t
  endif
  if |ub - t1| > |ub - t3|
    t = t1
    t1 = t3
    t3 = t
  endif
  if |ub - t1| > |ub - t2|
    t = t1
    t1 = t2
    t2 = t
  endif
  if @sheet == 0
    t = t0
  elseif @sheet == 1
    t = t1
  elseif @sheet == 2
    t = t2
  elseif @sheet == 3
    t = t3
  elseif @sheet == 4
    t = t0
    if imag(ub) > 0
      t = t1
    endif
  elseif @sheet == 5
    t = t1
    if imag(ub) > 0
      t = t2
    endif
  else
    t = t2
    if imag(ub) > 0
      t = t3
    endif
  endif
  complex an3 = 1/n3
  complex an2 = 1/n2
  complex an1 = 1/n1
  complex s = (an3*t*t - an2*t)/(an2*t - an1)
  complex p = ((u - s)/(an3 - (1 + s)*an2 + s*an1))^an2
  complex an2 = -an2*(1 + s)*p
  complex an1 = an1*s*p*p
  complex a0 = s*p
  z = 2*#pixel

loop:
  z = ((an3*z + an2)*z + an1)*z^(@n + 1) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet100_n_1"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param n
    caption = "Order"
    default = 1
    hint = "This defines the order of the fourth critical point."
  endparam
  param sheet
    caption = "Sheets"

    default = 0

    hint = "This has three sheets.  Choose bottom, middle, top, half \

            bottom half mid, or half mid half top."
  endparam
  param branchcut
    caption = "Branch Cut"
    default = (1,0)
    hint = "There are two sheets to this paramaritization. Use (-1,0) \
            to see the other sheet."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0

    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet100_n_1"
  power = power
  bailout = bailout
}

Meet10_1_0 {
; Generic Mandelbrot set
init:
  complex s = #pixel
  complex p = sqrt(6*s - 9)
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*p
  complex a0 = s*p
  z = a0
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Meet10_1_0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam

switch:
  type = "Jeet10_1_0"
  seed = #pixel
  power = power
  bailout = bailout
}


Jeet10_1_0 {

; Generic Julia set
init:

  complex s = @seed
  complex p = sqrt(6*s - 9)
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*p

  complex a0 = s*p
  z = #pixel*2
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jeet10_1_0"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam

  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Meet10_1_0"
  power = power
  bailout = bailout
}

Critfix {
; Generic Mandelbrot set
init:
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*#pixel

  z = #pixel
loop:
  z = (a3*z + a2)*sqr(z)
bailout:
  |z| <= @bailout
default:
  title = "Critfix"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jritfix"
  seed = #pixel

  power = power
  bailout = bailout
}


Jritfix {
; Generic Julia set
init:
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*@seed
  z = #pixel
loop:
  z = (a3*z + a2)*sqr(z)
bailout:
  |z| <= @bailout
default:
  title = "Jritfix"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."

  endparam
switch:
  type = "Critfix"
  power = power
  bailout = bailout


}

Critper3 {
; Generic Mandelbrot set
init:
  complex s = #pixel
;  s = 1 - 1/s
;  s = 1 - 1/s
  complex a3 = 0.3333333333333333333
  complex pp = (1/(s - s*s) - s)*3/s
  complex a0 = sqrt(pp)
  complex a2 = a0*((s - 1)/pp - a3)
  z = -2*a2
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Critper3"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jritper3"
  seed = #pixel
  power = power
  bailout = bailout
}


Jritper3 {
; Generic Julia set
init:
  complex s = @seed
;  s = 1 - 1/s
;  s = 1 - 1/s
  complex a3 = 0.3333333333333333333
  complex pp = (1/(s - s*s) - s)*3/s
  complex a0 = sqrt(pp)
  complex a2 = a0*((s - 1)/pp - a3)
  z = #pixel*2
loop:

  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jritper3"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."

  endparam
switch:
  type = "Critper3"
  power = power
  bailout = bailout
}

Cccritper3 {

; Generic Mandelbrot set
init:
  complex s = #pixel
  complex ca2 = -1.5 + s
  complex ca1 = -1.5 - s
  complex ca0 = 1
  complex cq = (3*ca1 - ca2*ca2)/9
  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
  if real(cr) < 0
    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  endif
  complex wi = cq/w
  complex s = w - wi - ca2/3
;  s = 1 - 1/s
;  s = 1 - 1/s
  complex a5 = 0.2
  complex a4 = -0.25
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5
  complex ss = sqr(s)
  complex smss = s - ss
  complex pppp = 10*(ss - s + 1)*(ss*(s - 2) - s + 1)/(smss*smss*smss)
  complex pp = sqrt(pppp)
  complex p = sqrt(pp)
  complex t = (60*(s - 1) + pppp*(3 - 5*s))/(pppp*5*(1 - 2*s))
  complex a4 = a4*p*(1 + t + s)
  complex a3 = a3*pp*(s + t + s*t)
  complex a2 = a2*p*pp*s*t
  z = t*p
loop:
  z = (((a5*z + a4)*z + a3)*z + a2)*sqr(z) + p
bailout:
  |z| <= @bailout


default:
  title = "Cccritper3"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jccritper3"
  seed = #pixel
  power = power
  bailout = bailout
}


Jccritper3 {
; Generic Julia set
init:
  complex s = @seed
  complex ca2 = -1.5 + s
  complex ca1 = -1.5 - s
  complex ca0 = 1
  complex cq = (3*ca1 - ca2*ca2)/9
  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
  if real(cr) < 0
    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)

  endif
  complex wi = cq/w
  complex s = w - wi - ca2/3

;  s = 1 - 1/s
;  s = 1 - 1/s
  complex a5 = 0.2
  complex a4 = -0.25
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5
  complex ss = sqr(s)
  complex smss = s - ss
  complex pppp = 10*(ss - s + 1)*(ss*(s - 2) - s + 1)/(smss*smss*smss)
  complex pp = sqrt(pppp)
  complex p = sqrt(pp)
  complex t = (60*(s - 1) + pppp*(3 - 5*s))/(pppp*5*(1 - 2*s))
  complex a4 = a4*p*(1 + t + s)
  complex a3 = a3*pp*(s + t + s*t)
  complex a2 = a2*p*pp*s*t
  z = #pixel*2
loop:
  z = (((a5*z + a4)*z + a3)*z + a2)*sqr(z) + p
bailout:
  |z| <= @bailout
default:
  title = "Jccritper3"
  param seed

    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0

    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:

  type = "Cccritper3"
  power = power
  bailout = bailout
}

Ccritper3 {
; Generic Mandelbrot set
init:
  complex s = #pixel
  complex a4 = 0.25
  complex a3 = -0.3333333333333333333
  complex a2 = 0.5
  complex ss = sqr(s)
  complex smss = s - ss
  complex ppp = 4*((2*s - 3)*(s - 1)*ss - 1)/(smss*smss)
  complex p = ppp^(1/3)
  complex t = 6*(s - 1)/ppp + 0.5
  complex a3 = a3*p*(1 + t)
  complex a2 = a2*p*p*t
  z = t*p
loop:
  z = ((a4*z + a3)*z + a2)*sqr(z) + p
bailout:
  |z| <= @bailout
default:
  title = "Ccritper3"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam

  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jcritper3"
  seed = #pixel
  power = power
  bailout = bailout
}



Jcritper3 {
; Generic Julia set
init:
  complex s = @seed
  complex a4 = 0.25
  complex a3 = -0.3333333333333333333
  complex a2 = 0.5
  complex ss = sqr(s)
  complex smss = s - ss
  complex ppp = 4*((2*s - 3)*(s - 1)*ss - 1)/(smss*smss)
  complex p = ppp^(1/3)
  complex t = 6*(s - 1)/ppp + 0.5
  complex a3 = a3*p*(1 + t)
  complex a2 = a2*p*p*t
  z = #pixel*2
loop:
  z = ((a4*z + a3)*z + a2)*sqr(z) + p
bailout:
  |z| <= @bailout
default:
  title = "Jcritper3"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam

switch:
  type = "Ccritper3"
  power = power
  bailout = bailout
}


Parab3 {
; Generic Mandelbrot set
init:

  complex angl = (sqrt(@start*@start+4)-@start)/2
  angl = 1/(@cfrac2 + angl)
  angl = 1/(@cfrac1 + angl)
  angl = exp(angl*#pi*(0,2))*@lambda
  complex a3 = 0.3333333333333333333
  complex a2 = sqrt(#pixel)
  complex sqterm = sqrt(#pixel - angl)
  z = -a2 + sqterm
  z2 = -a2 - sqterm

loop:
  z = ((a3*z + a2)*z + angl)*z
  z2 = ((a3*z2 + a2)*z2 + angl)*z2
  if |z2| > @bailout
    z = z2

  endif
bailout:
  |z| <= @bailout
default:
  title = "Parab3"
  center = (0, 0)
  param lambda
    caption = "Parabolic Multiplier"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param start
    caption = "Starting point"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac1
    caption = "Cont Frac 1"
    default = (0,0)

    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac2
    caption = "Cont Frac 2"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param startpix

    caption = "Start at Pix"
    default = true
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0

    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jarab3"
  seed = #pixel
  bailout = bailout
  lambda = lambda
  start = start
  cfrac1 = cfrac1
  cfrac2 = cfrac2
}


Jarab3 {
; Generic Julia set
init:

  complex angl = (sqrt(@start*@start+4)-@start)/2
  angl = 1/(@cfrac2 + angl)
  angl = 1/(@cfrac1 + angl)
  angl = exp(angl*#pi*(0,2))*@lambda
  complex a3 = 0.3333333333333333333
  complex a2 = sqrt(@seed)
  z = 2*#pixel
loop:
  z = ((a3*z + a2)*z + angl)*z
bailout:
  |z| <= @bailout
default:
  title = "Jarab3"
  param lambda
    caption = "Parabolic Multiplier"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param start
    caption = "Starting point"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac1
    caption = "Cont Frac 1"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac2
    caption = "Cont Frac 2"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."


  endparam
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."

  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Parab3"
  power = power
  bailout = bailout
}

Parabper2 {
; Generic Mandelbrot set
init:
  complex angl = (sqrt(@start*@start+4)-@start)/2
  angl = 1/(@cfrac2 + angl)
  angl = 1/(@cfrac1 + angl)
  angl = exp(angl*#pi*(0,2))*@lambda
  complex a3 = 0.3333333333333333333
  pp = #pixel
  complex a1 = (pp - 6 + sqrt(sqr(pp - 6) - 36*angl))/6
;  complex pp = 3*(a1 + 2 + angl/a1)
  complex m = 2*(pp + 3 + 3*a1)/(3*pp)
  complex a0 = sqrt(pp)
  complex a2 = -0.5*m*a0
  complex sqterm = sqrt(sqr(a2) - a1)
  z = -a2 + sqterm
  z2 = -a2 - sqterm
loop:
  z = ((a3*z + a2)*z + a1)*z + a0
  z2 = ((a3*z2 + a2)*z2 + a1)*z2 + a0
  if |z2| > @bailout
    z = z2
  endif
bailout:
  |z| <= @bailout
default:
  title = "Parabper2"
  center = (0, 0)
  param lambda
    caption = "Parabolic Multiplier"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param start
    caption = "Starting point"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac1
    caption = "Cont Frac 1"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac2
    caption = "Cont Frac 2"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param startpix
    caption = "Start at Pix"
    default = true
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0

    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jarabper2"
  seed = #pixel
  bailout = bailout
  lambda = lambda
  start = start
  cfrac1 = cfrac1




  cfrac2 = cfrac2
}



Jarabper2 {
; Generic Julia set
init:
  complex angl = (sqrt(@start*@start+4)-@start)/2
  angl = 1/(@cfrac2 + angl)
  angl = 1/(@cfrac1 + angl)
  angl = exp(angl*#pi*(0,2))*@lambda
  complex a3 = 0.3333333333333333333
  complex pp = @seed
  complex a1 = (pp - 6 + sqrt(sqr(pp - 6) - 36*angl))/6
;  complex pp = 3*(a1 + 2 + angl/a1)
  complex m = 2*(pp + 3 + 3*a1)/(3*pp)
  complex a0 = sqrt(pp)
  complex a2 = -0.5*m*a0
  z = 2*#pixel
loop:
  z = ((a3*z + a2)*z + a1)*z + a0
bailout:

  |z| <= @bailout
default:


  title = "Jarabper2"
  param lambda
    caption = "Parabolic Multiplier"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param start
    caption = "Starting point"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac1
    caption = "Cont Frac 1"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param cfrac2
    caption = "Cont Frac 2"
    default = (0,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Parabper2"
  power = power
  bailout = bailout
}

Rotate3 {
; Generic Mandelbrot set
init:
  complex a3 = 0.3333333333333333333
  z = sqrt(#pixel)
loop:
  z = (a3*sqr(z) - #pixel)*z

bailout:
  |z| <= @bailout
default:
  title = "Rotate3"
  center = (0, 0)
  param lambda
    caption = "Parabolic Multiplier"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param startpix
    caption = "Start at Pix"
    default = true
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0

    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:

  type = "Jotate3"

  seed = #pixel
  bailout = bailout
  lambda = lambda
}


Jotate3 {
; Generic Julia set
init:
  complex a3 = 0.3333333333333333333
  z = #pixel
loop:
  z = (a3*sqr(z) - @seed)*z
bailout:

  |z| <= @bailout
default:
  title = "Jotate3"
  param lambda
    caption = "Parabolic Multiplier"
    default = (1,0)

    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."

  endparam
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)

    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam

switch:
  type = "Rotate3"
  power = power
  bailout = bailout
}

Conjsym {
; Generic Mandelbrot set
init:
  complex a3 = 0.3333333333333333333
  complex p = sqrt(#pixel)
  complex a2 = -real(p)
  complex a1 = |p|
  z = p
loop:

  z = ((a3*z + a2)*z + a1)*z

bailout:
  |z| <= @bailout
default:
  title = "Conjsym"
  center = (0, 0)
  param lambda
    caption = "Parabolic Multiplier"
    default = (1,0)

    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param startpix
    caption = "Start at Pix"
    default = true
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jonjsym"
  seed = #pixel
  bailout = bailout
  lambda = lambda
}


Jonjsym {
; Generic Julia set
init:
  complex a3 = 0.3333333333333333333
  complex p = sqrt(@seed)
  complex a2 = -real(p)
  complex a1 = |p|
  z = #pixel
loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Jonjsym"

  param lambda
    caption = "Parabolic Multiplier"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param seed
    caption = "Julia seed"

    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Conjsym"
  power = power
  bailout = bailout
}

Leapfix {
; Generic Mandelbrot set
init:
  complex a3 = 0.3333333333333333333
  complex a2 = -2*#pixel
  complex a1 = 3*#pixel*#pixel
  z = #pixel
loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Leapfix"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \

            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jeapfix"
  seed = #pixel
  power = power
  bailout = bailout
}



Jeapfix {
; Generic Julia set
init:
  complex a3 = 0.3333333333333333333
  complex a2 = -2*@seed
  complex a1 = 3*@seed*@seed
  z = #pixel

loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Jeapfix"
  param seed

    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"


    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Leapfix"
  power = power
  bailout = bailout
}

Stepfix {
; Generic Mandelbrot set

init:
  complex a3 = 0.3333333333333333333
  complex opix = 3/(4*#pixel)
  complex xm1 = (#pixel + opix)/sqrt(3)

  complex p = (#pixel - opix)/xm1
  complex q = 2*(xm1 + 1)/p + a3*p
  complex a2 = -0.5*(p + q)
  complex a1 = p*q
  z = q
loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Stepfix"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jtepfix"
  seed = #pixel
  power = power
  bailout = bailout
}

Jtepfix {
; Generic Julia set
init:
  complex a3 = 0.3333333333333333333
  complex opix = 3/(4*@seed)
  complex xm1 = (@seed + opix)/sqrt(3)
  complex p = (@seed - opix)/xm1
  complex q = 2*(xm1 + 1)/p + a3*p
  complex a2 = -0.5*(p + q)
  complex a1 = p*q
  z = #pixel
loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Jtepfix"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"


    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam

switch:
  type = "Stepfix"
  power = power
  bailout = bailout
}

Stepfix2 {
; Generic Mandelbrot set
init:
  complex s = #pixel
  complex u = (2*sqr(s) - 3*s)/(3*s - 6)
  complex p = sqrt(6*s/(3*u - 1))
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*(1 + u)*p
  complex a1 = u*sqr(p)
  z = p*u
loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Stepfix2"
  center = (0, 0)

  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam

  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Jtepfix2"
  seed = #pixel
  power = power
  bailout = bailout
}

Jtepfix2 {
; Generic Julia set
init:
  complex s = @seed
  complex u = (2*sqr(s) - 3*s)/(3*s - 6)
  complex p = sqrt(6*s/(3*u - 1))
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*(1 + u)*p
  complex a1 = u*sqr(p)
  z = #pixel
loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Jtepfix2"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"


    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam

switch:
  type = "Stepfix2"
  power = power
  bailout = bailout
}

Stepper2 {
; Generic Mandelbrot set
init:
  complex s = #pixel
  complex p = sqrt(-3*sqr(s))
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*p
  complex a0 = p/s
  z = p
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Stepper2"

  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)

    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam

switch:
  type = "Jtepper2"
  seed = #pixel
  power = power
  bailout = bailout
}


Jtepper2 {
; Generic Julia set
init:
  complex s = @seed
  complex p = sqrt(-3*sqr(s))
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*p
  complex a0 = p/s
  z = #pixel*2
loop:
  z = (a3*z + a2)*sqr(z) + a0
bailout:
  |z| <= @bailout
default:
  title = "Jtepper2"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam

  param power
    caption = "Power"


    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0

    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam


switch:
  type = "Stepper2"
  power = power
  bailout = bailout
}

Stepfix3 {
; Generic Mandelbrot set
init:
  complex t = #pixel
  complex s = 0
  complex cr1 = 0.5*(flip(sqrt(3)) - 1)
  complex cr2 = sqr(cr1)
  complex t2 = sqr(t)
  complex ca2 = (t - 2)*t2 - 2
  complex ca1 = 1 + (3 - t2)*t2
  complex ca0 = (2*t2 - 3*t)*t2
  complex cq = (3*ca1 - ca2*ca2)/9
  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
  if real(cr) < 0
    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)

  endif
  complex wi = cq/w
  complex s0 = w - wi
  complex s1 = w*cr1 - wi*cr2
  complex s2 = w*cr2 - wi*cr1
  if |s0| > |s1|
    s = s0
    s0 = s1


    s1 = s
  endif
  if |s0| > |s2|
    s = s0
    s0 = s2
    s2 = s
  endif
  if |s1| > |s2|
    s = s1
    s1 = s2
    s2 = s
  endif
  s = s1
  if @sheet == 0
    s = s0
  elseif @sheet == 1

    s = s1
  elseif @sheet == 2
    s = s2
  elseif @sheet == 4
    if imag(t) > 0
      s = s0
    endif
  else
    if imag(t) > 0
      s = s2
    endif
  endif
  complex s = s - ca2/3
  complex u = (2*sqr(s) - 3*s)/(3*s - 6)
  complex p = sqrt(6*t/(3*u - 1))
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*(1 + u)*p
  complex a1 = u*sqr(p)
  z = p*u
loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:

  |z| <= @bailout
default:
  title = "Stepfix3"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."

  endparam
  param sheet
    caption = "Sheets"
    default = 3
    hint = "This has three sheets.  Choose bottom, middle, top, half \
            bottom half mid, or half mid half top."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam

switch:
  type = "Jtepfix3"
  seed = #pixel
  sheet = sheet

  bailout = bailout
}

Jtepfix3 {
; Generic Julia set
init:
  complex t = @seed
  complex s = 0
  complex cr1 = 0.5*(flip(sqrt(3)) - 1)
  complex cr2 = sqr(cr1)

  complex t2 = sqr(t)
  complex ca2 = (t - 2)*t2 - 2
  complex ca1 = 1 + (3 - t2)*t2
  complex ca0 = (2*t2 - 3*t)*t2
  complex cq = (3*ca1 - ca2*ca2)/9
  complex cr = (9*ca2*ca1 - 27*ca0 - 2*ca2*ca2*ca2)/54
  if real(cr) < 0
    complex w = (cr - sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  else
    complex w = (cr + sqrt(sqr(cr) + cq*sqr(cq)))^(1/3)
  endif

  complex wi = cq/w
  complex s0 = w - wi
  complex s1 = w*cr1 - wi*cr2
  complex s2 = w*cr2 - wi*cr1
  if |s0| > |s1|
    s = s0
    s0 = s1
    s1 = s
  endif
  if |s0| > |s2|
    s = s0
    s0 = s2
    s2 = s
  endif
  if |s1| > |s2|
    s = s1
    s1 = s2
    s2 = s
  endif
  s = s1
  if @sheet == 0
    s = s0
  elseif @sheet == 1
    s = s1
  elseif @sheet == 2
    s = s2
  elseif @sheet == 4
    if imag(t) > 0
      s = s0
    endif
  else
    if imag(t) > 0
      s = s2
    endif
  endif
  complex s = s - ca2/3
  complex u = (2*sqr(s) - 3*s)/(3*s - 6)
  complex p = sqrt(6*t/(3*u - 1))
  complex a3 = 0.3333333333333333333
  complex a2 = -0.5*(1 + u)*p
  complex a1 = u*sqr(p)
  z = #pixel
loop:
  z = ((a3*z + a2)*z + a1)*z
bailout:
  |z| <= @bailout
default:
  title = "Jtepfix3"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param sheet
    caption = "Sheets"
    default = 3
    hint = "This has three sheets.  Choose bottom, middle, top, half \
            bottom half mid, or half mid half top."
  endparam
  param power
    caption = "Power"


    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam

switch:
  type = "Stepfix3"
  power = power
  bailout = bailout
}

Three2two {
; Generic Mandelbrot set
init:
  complex a = -6*#pixel*#pixel
  complex b = 8*#pixel*#pixel*#pixel
  complex c = -3*sqr(sqr(#pixel)) - 2*#pixel
  z = @start*#pixel
loop:
  z = sqr(sqr(z)) + a*sqr(z) + b*z + c
bailout:
  |z| <= @bailout
default:
  title = "Three2two"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (1,0)
    hint = "Perturbation. Use (1,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Mandelbrot set. Use (1,0) \
            for the standard Mandelbrot set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Phree2two"
  seed = #pixel
  power = power
  bailout = bailout
}


Phree2two {
; Generic Julia set
init:
  complex a = -6*@seed*@seed
  complex b = 8*@seed*@seed*@seed
  complex c = -3*sqr(sqr(@seed)) - 2*@seed
  z = #pixel
loop:
  z = sqr(sqr(z)) + a*sqr(z) + b*z + c
bailout:
  |z| <= @bailout
default:
  title = "Phree2two"
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."

  endparam
  param power
    caption = "Power"
    default = (1,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Three2two"
  power = power
  bailout = bailout
}

Elephant {
; Limit Zoom of Mandelbrot set
init:
  bool indeep = true
  float itoffset = 0
  float dives = 1
  z = @start + #pixel
loop:
  if indeep
    float offstep = round(real(z))
    itoffset = itoffset - offstep - 1
    w = z - offstep
    if abs(imag(w)) < 2.8
      if imag(w) < 0
        v = conj(w) - flip(2.5)
      else
        v = w - flip(2.5)
      endif
      u = (-9.748504903269681800e+000, 2.259406621999715100e+000) + v*(\

          (9.066551936825199000e-001, -2.074036912056804700e-002) + v*(\
          (-3.805799272742944400e-003, -1.681810353755348100e-003) + v*(\

          (-1.894938525219343400e-004, -1.302399607326304500e-004) + v*(\
          (-9.820676162509018900e-006, -9.700372281676589600e-006) + v*(\
          (-5.009257444112947900e-007, -6.975630290977511300e-007) + v*(\
          (-2.419924187157992000e-008, -4.854092718027711000e-008) + v*(\
          (-1.053944888602629400e-009, -3.273170060340258300e-009) + v*(\
          (-3.708112447306889500e-011, -2.140962484898100300e-010) + v*(\
          (-6.130111067563060900e-013, -1.359937108405049500e-011) + v*(\

          (5.360928355699816400e-014, -8.404644516378927200e-013) + v*(\
          (7.571979062819036800e-015, -5.072519731879296900e-014) + v*\
          (6.043020754909982700e-016, -3.011389687670057400e-015))))))))))))
      if imag(w) < 0
        z = 0.5*(conj(u) - 1)/(conj(u) + 1)
      else
        z = 0.5*(u - 1)/(u + 1)
      endif
      itoffset = itoffset - 12
      indeep = false
    elseif imag(w) > 10
      if imag(#pixel) < #pi
        float bigleap = ceil((imag(w) - 10)/(#pi - imag(#pixel)))
        dives = dives + bigleap
        z = w + bigleap*(#pixel - flip(#pi))

      endif
    elseif imag(w) < -10
      if imag(#pixel) > -#pi
        float bigleap = ceil((imag(w) + 10)/(-#pi - imag(#pixel)))
        dives = dives + bigleap
        z = w + bigleap*(#pixel + flip(#pi))
      endif
    else
      if imag(w) < 0
        v = exp(2*#pi*(0,1)*(conj(w) - flip(2.6)))
      else
        v = exp(2*#pi*(0,1)*(w - flip(2.6)))

      endif
      u = v*(\
          (-1.771574422374822400e+000, 3.008158248718677500e-001) + v*(\
          (1.161247798855508100e+000, 1.060150347288251200e-001) + v*(\
          (-6.186486776521550300e-001, -1.823642041315733100e-001) + v*(\
          (3.150728651773144200e-001, 1.671571437687602900e-001) + v*(\
          (-1.508025170404382100e-001, -1.222711022593431100e-001) + v*(\
          (6.763170397465391400e-002, 8.111202917057371000e-002) + v*(\
          (-2.754198423864979300e-002, -5.019684071459873400e-002) + v*(\
          (9.426710531076781100e-003, 2.954351158578514800e-002) + v*(\
          (-1.945294976491386600e-003, -1.666645207806186100e-002) + v*(\
          (-6.918190444668266900e-004, 9.047294640745664000e-003) + v*(\
          (1.301997331051690500e-003, -4.728449782213820600e-003) + v*(\
          (-1.178791499364848500e-003, 2.373391527693483800e-003) + v*(\
          (8.699587806287360200e-004, -1.136825824027341700e-003) + v*(\
          (-5.784523251938663300e-004, 5.129463920949076700e-004) + v*\
          (3.594977319353187400e-004, -2.122520653691554400e-004)))))))))))))))
      if imag(w) < 0
        z = w + conj(u) + flip(#pi) + #pixel
      else
        z = w + u - flip(#pi) + #pixel
      endif
      dives = dives + 1

    endif
  elseif |z - 0.51| < 0.01 && real(z) < 0.56
    w = (1 + 2*z)/(1 - 2*z)
    v = 1/w
    u = v*(\
        -5.000000000000000000e-001 + v*(\
        3.333333333333333700e-001 + v*(\
        -1.388888888888888700e-001 + v*(\
        1.375000000000000400e-001 + v*(\
        -9.055555555555550000e-002 + v*(\
        6.137566137566145100e-002 + v*(\
        -8.058390022675728000e-002 + v*(\
        4.564318783068788100e-002 + v*(\
        -1.297251616696071300e-002 + v*(\
        1.087715247715244500e-001 + v*(\
        -2.769523335811253600e-002 + v*(\
        -2.206830521587462600e-001 + v*(\
        -4.967267290859304600e-001 + v*(\
        5.171815482745201200e-001 + v*(\

        3.597365161478478500e+000 + v*\
        3.236962427432480600e+000)))))))))))))))
    if real(w) > 0 || abs(imag(w)) > 10
      z = #pixel + w - log(w) + u
      dives = dives + 1
    else
      z = w - log(-w) + u
    endif
    itoffset = itoffset - 1
    indeep = true
  else
    z = sqr(z) + 0.25
  endif
bailout:
  indeep || (|z| <= @bailout)
default:
  title = "Elephant"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (0.76799378613615426,0)
    hint = "Perturbation. Use (0.76799378613615426,0) for \
            the standard Mandelbrot set."
  endparam
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (2,0)
    hint = "This defines the power of the Julia set. Use (2,0) \

            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "Julphant"
  seed = #pixel
  power = power
  bailout = bailout
}

Julphant {
; Julia Sets for Limit Zooms of Mandelbrot set
init:
  bool indeep = @deepness
  float itoffset = 0
  float dives = 0
  z = #pixel
loop:
  if indeep

    float offstep = round(real(z))
    itoffset = itoffset - offstep - 1
    w = z - offstep

    if abs(imag(w)) < 2.8
      if imag(w) < 0
        v = conj(w) - flip(2.5)
      else
        v = w - flip(2.5)
      endif
      u = (-9.748504903269681800e+000, 2.259406621999715100e+000) + v*(\
          (9.066551936825199000e-001, -2.074036912056804700e-002) + v*(\
          (-3.805799272742944400e-003, -1.681810353755348100e-003) + v*(\
          (-1.894938525219343400e-004, -1.302399607326304500e-004) + v*(\

          (-9.820676162509018900e-006, -9.700372281676589600e-006) + v*(\

          (-5.009257444112947900e-007, -6.975630290977511300e-007) + v*(\
          (-2.419924187157992000e-008, -4.854092718027711000e-008) + v*(\
          (-1.053944888602629400e-009, -3.273170060340258300e-009) + v*(\
          (-3.708112447306889500e-011, -2.140962484898100300e-010) + v*(\
          (-6.130111067563060900e-013, -1.359937108405049500e-011) + v*(\
          (5.360928355699816400e-014, -8.404644516378927200e-013) + v*(\
          (7.571979062819036800e-015, -5.072519731879296900e-014) + v*\
          (6.043020754909982700e-016, -3.011389687670057400e-015))))))))))))
      if imag(w) < 0
        z = 0.5*(conj(u) - 1)/(conj(u) + 1)
      else
        z = 0.5*(u - 1)/(u + 1)
      endif
      itoffset = itoffset - 12
      indeep = false
    elseif imag(w) > 10
      if imag(@seed) < #pi
        if @bigon
          float bigleap = ceil((imag(w) - 10)/(#pi - imag(@seed)))
          dives = dives + bigleap
          z = w + bigleap*(@seed - flip(#pi))
        else
          dives = dives + 1
          z = w + @seed - flip(#pi)
        endif
      endif
    elseif imag(w) < -10
      if imag(@seed) > -#pi
        if @bigon
          float bigleap = ceil((imag(w) + 10)/(-#pi - imag(@seed)))
          dives = dives + bigleap
          z = w + bigleap*(@seed + flip(#pi))
        else
          dives = dives + 1
          z = w + @seed + flip(#pi)
        endif
      endif

    else
      if imag(w) < 0
        v = exp(2*#pi*(0,1)*(conj(w) - flip(2.6)))
      else
        v = exp(2*#pi*(0,1)*(w - flip(2.6)))
      endif
      u = v*(\
          (-1.771574422374822400e+000, 3.008158248718677500e-001) + v*(\
          (1.161247798855508100e+000, 1.060150347288251200e-001) + v*(\
          (-6.186486776521550300e-001, -1.823642041315733100e-001) + v*(\
          (3.150728651773144200e-001, 1.671571437687602900e-001) + v*(\
          (-1.508025170404382100e-001, -1.222711022593431100e-001) + v*(\
          (6.763170397465391400e-002, 8.111202917057371000e-002) + v*(\
          (-2.754198423864979300e-002, -5.019684071459873400e-002) + v*(\
          (9.426710531076781100e-003, 2.954351158578514800e-002) + v*(\
          (-1.945294976491386600e-003, -1.666645207806186100e-002) + v*(\
          (-6.918190444668266900e-004, 9.047294640745664000e-003) + v*(\

          (1.301997331051690500e-003, -4.728449782213820600e-003) + v*(\
          (-1.178791499364848500e-003, 2.373391527693483800e-003) + v*(\
          (8.699587806287360200e-004, -1.136825824027341700e-003) + v*(\
          (-5.784523251938663300e-004, 5.129463920949076700e-004) + v*\
          (3.594977319353187400e-004, -2.122520653691554400e-004)))))))))))))))
      if imag(w) < 0

        z = w + conj(u) + flip(#pi) + @seed
      else
        z = w + u - flip(#pi) + @seed
      endif
      dives = dives + 1
    endif
  elseif |z - 0.51| < 0.01 && real(z) < 0.56
    w = (1 + 2*z)/(1 - 2*z)
    v = 1/w
    u = v*(\
        -5.000000000000000000e-001 + v*(\
        3.333333333333333700e-001 + v*(\
        -1.388888888888888700e-001 + v*(\
        1.375000000000000400e-001 + v*(\
        -9.055555555555550000e-002 + v*(\
        6.137566137566145100e-002 + v*(\
        -8.058390022675728000e-002 + v*(\
        4.564318783068788100e-002 + v*(\
        -1.297251616696071300e-002 + v*(\
        1.087715247715244500e-001 + v*(\
        -2.769523335811253600e-002 + v*(\
        -2.206830521587462600e-001 + v*(\
        -4.967267290859304600e-001 + v*(\
        5.171815482745201200e-001 + v*(\
        3.597365161478478500e+000 + v*\
        3.236962427432480600e+000)))))))))))))))
    if real(w) > 0 || abs(imag(w)) > 10
      z = @seed + w - log(w) + u
      dives = dives + 1
    else
      z = w - log(-w) + u
    endif
    itoffset = itoffset - 1
    indeep = true
  else
    z = sqr(z) + 0.25
  endif
bailout:
  indeep || (|z| <= @bailout)
default:
  title = "Julphant"


  center = (0, 0)
  param start
    caption = "Starting point"
    default = (0,0)
    hint = "Perturbation. Use (0,0) for the standard Mandelbrot set."
  endparam

  param deepness
    caption = "Start Deep"
    default = false
    hint = "View the Julia set from a normal viewpoint or \
            from the depths of the parabolic point."
  endparam
  param bigon
    caption = "Big Leaps"

    default = true
    hint = "Big leaps have a buggy interaction with Julphant\
            and coloring dives.  Match this to Coloring Big Leaps"
  endparam
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \

            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (2,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 128.0
    min = 1.0
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
}

Elerev0 {
; Limit Zoom of Mandelbrot set
init:
  bool indeep = false
  float itoffset = 0
  float dives = 0
  z = @start
loop:
  if indeep
    float offstep = round(real(z))
    itoffset = itoffset - offstep - 1
    w = z - offstep
    if abs(imag(w)) < 2.8
      if imag(w) < 0
        v = conj(w) - 2.5
      else
        v = w - 2.5
      endif

      u = (-9.748504903269681800e+000, 2.259406621999715100e+000) + v*(\

          (9.066551936825199000e-001, -2.074036912056804700e-002) + v*(\
          (-3.805799272742944400e-003, -1.681810353755348100e-003) + v*(\
          (-1.894938525219343400e-004, -1.302399607326304500e-004) + v*(\
          (-9.820676162509018900e-006, -9.700372281676589600e-006) + v*(\
          (-5.009257444112947900e-007, -6.975630290977511300e-007) + v*(\
          (-2.419924187157992000e-008, -4.854092718027711000e-008) + v*(\
          (-1.053944888602629400e-009, -3.273170060340258300e-009) + v*(\
          (-3.708112447306889500e-011, -2.140962484898100300e-010) + v*(\
          (-6.130111067563060900e-013, -1.359937108405049500e-011) + v*(\
          (5.360928355699816400e-014, -8.404644516378927200e-013) + v*(\
          (7.571979062819036800e-015, -5.072519731879296900e-014) + v*\
          (6.043020754909982700e-016, -3.011389687670057400e-015))))))))))))
      if imag(w) < 0
        z = 0.5*(conj(u) - 1)/(conj(u) + 1)
      else
        z = 0.5*(u - 1)/(u + 1)
      endif
      itoffset = itoffset - 12
      indeep = false
    elseif imag(w) > 10
      if imag(#pixel) < #pi
        float bigleap = ceil((imag(w) - 10)/(#pi - imag(#pixel)))
        dives = dives + bigleap
        z = w + bigleap*(#pixel - flip(#pi))
      endif
    elseif imag(w) < -10
      if imag(#pixel) > -#pi

        float bigleap = ceil((imag(w) + 10)/(-#pi - imag(#pixel)))

        dives = dives + bigleap
        z = w + bigleap*(#pixel + flip(#pi))
      endif
    else
      if imag(w) < 0
        v = exp(2*#pi*(0,1)*(conj(w) - 2.6))
      else
        v = exp(2*#pi*(0,1)*(w - 2.6))
      endif
      u = v*(\
          (-1.771574422374822400e+000, 3.008158248718677500e-001) + v*(\
          (1.161247798855508100e+000, 1.060150347288251200e-001) + v*(\
          (-6.186486776521550300e-001, -1.823642041315733100e-001) + v*(\
          (3.150728651773144200e-001, 1.671571437687602900e-001) + v*(\
          (-1.508025170404382100e-001, -1.222711022593431100e-001) + v*(\
          (6.763170397465391400e-002, 8.111202917057371000e-002) + v*(\

          (-2.754198423864979300e-002, -5.019684071459873400e-002) + v*(\
          (9.426710531076781100e-003, 2.954351158578514800e-002) + v*(\
          (-1.945294976491386600e-003, -1.666645207806186100e-002) + v*(\
          (-6.918190444668266900e-004, 9.047294640745664000e-003) + v*(\
          (1.301997331051690500e-003, -4.728449782213820600e-003) + v*(\
          (-1.178791499364848500e-003, 2.373391527693483800e-003) + v*(\
          (8.699587806287360200e-004, -1.136825824027341700e-003) + v*(\
          (-5.784523251938663300e-004, 5.129463920949076700e-004) + v*\
          (3.594977319353187400e-004, -2.122520653691554400e-004)))))))))))))))
      if imag(w) < 0
        z = w + conj(u) + flip(#pi) + #pixel
      else
        z = w + u - flip(#pi) + #pixel
      endif
      dives = dives + 1

    endif
  elseif |z - 0.51| < 0.01 && real(z) < 0.56
    w = (1 + 2*z)/(1 - 2*z)
    v = 1/w
    u = v*(\
        -5.000000000000000000e-001 + v*(\
        3.333333333333333700e-001 + v*(\

        -1.388888888888888700e-001 + v*(\
        1.375000000000000400e-001 + v*(\
        -9.055555555555550000e-002 + v*(\
        6.137566137566145100e-002 + v*(\
        -8.058390022675728000e-002 + v*(\
        4.564318783068788100e-002 + v*(\
        -1.297251616696071300e-002 + v*(\
        1.087715247715244500e-001 + v*(\

        -2.769523335811253600e-002 + v*(\
        -2.206830521587462600e-001 + v*(\
        -4.967267290859304600e-001 + v*(\
        5.171815482745201200e-001 + v*(\
        3.597365161478478500e+000 + v*\
        3.236962427432480600e+000)))))))))))))))
    if real(w) > 0 || abs(imag(w)) > 10
      z = #pixel + w - log(w) + u
      dives = dives + 1
    else
      z = w - log(-w) + u
    endif
    itoffset = itoffset - 1
    indeep = true

  else
    z = sqr(z) + 0.25
  endif
bailout:
  (|z| <= @bailout)
default:
  title = "Elerev0"
  center = (0, 0)
  param start
    caption = "Starting point"
    default = (0,0)
    hint = "Perturbation. Use (0,0) for the standard Mandelbrot set."
  endparam
  param seed
    caption = "Julia seed"
    default = (0, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param power
    caption = "Power"
    default = (2,0)
    hint = "This defines the power of the Julia set. Use (2,0) \
            for the standard Julia set."
  endparam
  param bailout
    caption = "Bailout value"
    default = 20.0
    min = 1.0

    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
}