Bailey {
;
;Bailey is method for solving ecuations similar to Newton
;It usualy requires less iterations, but the formula used is a bit more difficult.
;On the average the time needed to reach a solution should be quite similar for both methods.
;
init:
  z = pixel
  complex f
  complex fp
  complex fs

loop:
  zold = z
  f=z^@p1 - @r
  fp=@p1*z^(@p1-1)
  fs=(@p1-1)*@p1*z^(@p1-2)
  z=z - f/(fp-(f*fs/2/fp))
bailout:
  |z - zold|/|z| >= @bail
default:
  title = "Bailey"
  maxiter = 100

  param p1
    caption = "Exponent"
    default = (3,0)
    hint = "Specifies the exponent of the equation that is solved by \
            Bayley's method. Use real numbers (set the imaginary component \
            to zero) to obtain classic Newton fractals."
  endparam

  param r
    caption = "Root"
    default = (1,0)
    hint = "Specifies the root of the equation that is solved. Use larger \
            numbers for slower convergence."
  endparam
  
  param bail
    caption = "Bailout"
    default = 0.00001
    hint = "Bailout value"
  endparam

}

Newton {
;Just a tipical Polinomial Newton fractal
;the polinom goes up to the 10th power coeficients. 
global:

  
init:
complex oldz=9999999
complex z=#pixel
complex f
complex fp
  
loop:
oldz=z
f = @a0*z^0 + @a1*z^1 + @a2*z^2 + @a3*z^3 + @a4*z^4 + @a5*z^5 + @a6*z^6 + @a7*z^7 + @a8*z^8 + @a9*z^9 + @a10*z^10
fp = @a1*z^0 + 2*@a2*z^1 + 3*@a3*z^2 + 4*@a4*z^3 + 5*@a5*z^4 + 6*@a6*z^5 + 7*@a7*z^6 + 8*@a8*z^7 + 9*@a9*z^8 + 10*@a10*z^9
z=z-(f/fp)
  
bailout:
|z-oldz|>@bail

  
default:
  title = "Newton"
float param bail
  caption="bailout"
  default=0.0000001
  endparam
float param a0
  caption="a0"
  default=0
  endparam
float param a1
  caption="a1"
  default=0
  endparam
float param a2
  caption="a2"
  default=0
  endparam
float param a3
  caption="a3"
  default=0
  endparam
float param a4
  caption="a4"
  default=0
  endparam
float param a5
  caption="a5"
  default=0
  endparam
float param a6
  caption="a6"
  default=0
  endparam
float param a7
  caption="a7"
  default=0
  endparam
float param a8
  caption="a8"
  default=0
  endparam
float param a9
  caption="a9"
  default=0
  endparam
float param a10
  caption="a10"
  default=0
  endparam
  
}