ifs-leaf-m { 
init:
  a0 = real(@a), b0 = real(@b), c0 = real(@c), d0 = real(@d),m0 = real(@m)
  a1 = imag(@a), b1 = imag(@b), c1 = imag(@c), d1 = imag(@d),m1 = imag(@m)
  n0 = real(@n),al0 = real(@al), k0 = real(@k), l0 = real(@l)
  n1 = imag(@n),al1 = imag(@al), k1 = imag(@k), l1 = imag(@l)
  z = #pixel
loop:
  x = @fn1(real(z))
  y = @fn2(imag(z))
  if(@type!=0)
    if(@type==1)
      a0 = -0.21053, b0 = -0.93117, c0 = -0.31579, d0 = 0.21862 ,m0=0,n0=0 
      a1 = 0.89474, b1 = -0.23482, c0=0.0,  d1=0.84615 ,m1=0,n1=0
      al0 = -0.34008,k0 = -6.00400, l0 = -2.53258
      al1 = 0.75709, k1 = -0.82044, l1 = -0.99777
    elseif @type==2
      a0 = 0.82407, b0 = 0.28148, c0 = -0.21235, d0 = 0.86420,m0=0,n0=0
      a1 = 0.08827, b1 = 0.52099, c1 = -0.46389, d1 = -0.37778,m1=0,n1=0
      al0 = 0.77193, k0 = 1.59554, l0 = 0.49085
      al1 = 0.20833, k1 = 4.51450, l1 = -1.07895
    elseif @type==3
      IF (imag(z)>@orbit)
        a0=2,b0=0,c0=0,d0=2,a1=2,b1=0,c1=0,d1=2,m0=0,n0=0
        al0=1,k0=0,l0=-2*@orbit,al1=1,k1=0,l1=-2*@orbit,m1=0,n1=0
      ELSEIF (real(z)>@orbit)
        a0=2,b0=0,c0=0,d0=2,a1=2,b1=0,c1=0,d1=2,m0=0,n0=0
        al0=1,k0=-2*@orbit,l0=0,al1=1,k1=-2*@orbit,l1=0,m1=0,n1=0
      ELSE
        a0=2,b0=0,c0=0,d0=2,a1=2,b1=0,c1=0,d1=2,m0=0,n0=0
        al0=1,k0=0,l0=0,al1=1,k1=0,l1=0,m1=0,n1=0
      ENDIF
    elseif @type==4
      IF (imag(z)>@orbit)
        l0=-l0,l1=-l1
      ELSEIF (real(z)>@orbit)
        k0=-k0,k1=-k1
      ELSE
        k0=k0,l0=l0,k1=k0,l1=l0
      ENDIF
    elseif @type==5
      a0=0,c0=-c0,d0=-d0*x,a1=0,c1=-c1,d1=-d1*x
      al0=1,k0=1,l0=0,al1=1,k1=1,l1=0
    endif
  endif 
  o0 = (d0 * x - b0 * y + n0*x*y + k0) / al0 + flip((-c0 * x + a0 * y + m0*x*y + l0) / al0)
  o1 = (d1 * x - b1 * y + n1*x*y + k1) / al1 + flip((-c1 * x + a1 * y + m1*x*y + l1) / al1)
  if @mode
    op0 = |o0 - @c|
    op1 = |o1 - @c|
  else
    op0 = |o0 - #pixel|
    op1 = |o1 - #pixel|
  endif
  if (|op0| <= |op1|)
    z = o0
  else
    z = o1
  endif
bailout:  
  |z| <= @bailout
default:
  title = "IFS Leaf Mset"  
  center = (0,4)
  magn = 0.2
  param type
    caption="IFS type"
    default=0
    enum="user type""type 2""type 3""Sierpinksi Triangle""test""henon(b,c,d are used)"
  endparam
  param mode
    caption="Mode"
    default=true
  endparam  
  param c
    caption = "Julia seed"
    default = (0,0)
  endparam
  param bailout
    caption = "Bailout value"
    default = 1000.0
  endparam
  param orbit
    caption="Orbit value"
    default=5
  endparam
  param a
    caption="Imag(y) value"
    default=(0.74546,-0.42424)
  endparam
  param b
    caption="Real(y) value"
    default=(-0.36460,0.65969)
  endparam
  param c
    caption="Imag(x) value"
    default=(0.40606,-0.17576)
  endparam
  param d
    caption="real(y) value"
    default=(0.51996,-0.41768)
  endparam
  param m
    caption="Imag(x*y)"
    default=(1.75,0.0)
  endparam
  param n
    caption="Real(x*y)"
    default=(0.0,0.0)
  endparam
  param k
    caption="Real(R) value"
    default=(-0.89714,4.62115)
  endparam
  param al
    caption="Divide value"
    default=(0.53566,0.29314)
  endparam
  param l
    caption="Imag(R) value"
    default=(-2.74193,2.78720)
  endparam
  func fn1
    caption="X Input function"
    default=ident()
  endfunc
  func fn2
    caption="Y Input function"
    default=ident()
  endfunc
}
e {
init:
  alpha=(sqrt(5)-1)/2
  power=2*pi*@n*alpha
  r=@fn1(power)
  z=#pixel
loop:
  z=z^2+r*z
bailout:
  |z|>@bailout
default:
  title = "e"
  param n
    caption="Power Value"
    default=(2,0)
  endparam
  param bailout
    caption="Bailout Valut"
    default=1000.0
  endparam
  func fn1
    caption="function about R"
    default=exp()
  endfunc
}

newton--z*e^z-1=0 {
init:
  z=#pixel
  complex zold=0.0
loop:
  zold=z
  z=z-(z-e^z)/(1+z)  
bailout:
  |z-zold|>=@bailout
default:
  title = "newton--z*e^n-1=0"
  param bailout
    caption="bailout value"
    default=0.00001
  endparam
}

newton {
init:
  complex z1=0
  complex z2=0
  complex z3=0
  complex p=0
  complex q=0
  complex zold=0
  z=#pixel
loop:
  zold=z
  z1=z-1
  z2=z+0.5
  z3=sqr(z)+1
  p=z1*z2*z3
  q=z2*z3+z1*z3+2*z*z1*z2
  z=z-p/(q+imag(@s))
bailout:
  |z-zold|>@bailout
default:
  title = "newton"
  param s
    caption="Value S"
    default=(0,1.25)
  endparam
  param bailout
    caption="bailout value"
    default=0.000001
  endparam
}

newton-z^n-1 {
init:
  z=#pixel
  complex zold=0.0
loop:
  zold=z
  z=((@n-1)*z^@n+@a)/(@n*z^(@n-1))  
bailout:
  |z-zold|>=@bailout
default:
  title = "newton-z^n-1"
  param bailout
    caption="bailout value"
    default=0.00001
  endparam
  param n
    caption="Value N"
    default=(3,0)
  endparam
  param s
    caption="Value S"
    default=(0,-0.5)
  endparam
  param a
    caption="Value A"
    default=(1,0)
  endparam
}

newton--P1,p2 {
init:
  z=#pixel
  complex z1=0
  complex z2=0
  complex z3=0
  complex z4=0
  complex p=0
  complex q=0
  complex m=0
  complex n=0
  complex zold=0
loop:
  zold=z
  z1=z+@s3
  z2=z+@s4
  z3=z^@f1+@s5
  z31=@f1*z^(@f1-1)
  z4=z^@f2+z^@f3+@s6
  z41=@f2*z^(@f2-1)+@f3*z^(@f3-1)
  p=z1*z2*z3
  q=z1*z4
  m=z2*z3+z1*z3+z31*z1*z2
  n=z4+z41*z1
  z=z+@a*q/(n+@fn1(@s1))+(1-@a)*p/(m-@fn2(@s2))
bailout:
  |z-zold|>=@bailout
default:
  title = "newton--(p1,p2)"
  param bailout
    caption="bailout value"
    default=0.154
    hint="(0.01-1)"
  endparam
  param a
    caption="Value A (0-1)"
    default=0.1
  endparam
  param s1
    caption="Imag S1"
    default=(0,0.25)
  endparam
  param s2
    caption="Imag S2"
    default=(0,-0.5)
  endparam
  param s3
    caption="Value S3"
    default=(-1,0)
    hint="重要参数"
  endparam
  param s4
    caption="Value S4"
    default=(0.5,0)
    hint="重要参数"
  endparam
  param s5
    caption="Value S5"
    default=(1,0)
    hint="可微调图形形状，取值范围很大"
  endparam
  param s6
    caption="Value S6"
    default=(1.25,0)
    hint="可微调图形形状，取值范围很大"
  endparam
  param f1
    caption="power f1"
    default=(2,0)
    hint="重要参数，取值不能太大"
  endparam
  param f2
    caption="power f2"
    default=(2,0)
    hint="重要参数，取值不能太大"
  endparam
  param f3
    caption="power f3"
    default=(1,0)
    hint="重要参数，取值不能太大"
  endparam 
  func fn1
    caption="function 1"
    default=ident()
    hint="对图形影响不大"
  endfunc
  func fn2
    caption="function 2"
    default=ident()
    hint="对图形影响不大"
  endfunc
}

Weierstrass {
init:
  complex w=(0,0)
  complex sum=(0,0)
  complex t=@paramt
loop:
  n=#z
  r=@param1
  s=@param2-2
  sum=sum+w  
  w=r^(s*n)*(1-@fn1(imag(r^n*t)))*@fn1(imag(@phi))
bailout:
  |w|>=|@bailout|
default:
  title = "Weierstrass"
  param paramt
    caption="函数初始值"
    default=(0,0)
  endparam
  param param1
    caption="参数 1"
   default=(2,0)
   hint="取值大于 1"
  endparam
  param param2
    caption="参数 2"
    default=1.34
    hint="取值在 1～2 之间"
  endparam
  param phi
    caption="参数 φ"
    default=2
    hint="取值任意"
  endparam
  param bailout
    caption="bailout valut"
    default=(1000.0,0)
  endparam
  func fn1
    caption="函数 1"
    default=exp()
  endfunc
}

weierstrass-01 {
init:
  int n=0
  z=#pixel
  complex sum=0.0
loop:
  n=n+1
  sum=sum+z
  z=(@param1^(@s*n-2*n))*@fn(@param1^n*z)
bailout:
  |sum|<@bailout1&&|z|>@bailout2
default:
  title = "weierstrass-01"
  param param1
    caption="Valut param 1"
    default=2.0
    hint="param > 1"
  endparam
  param s
    caption="valut S"
    default=1.45
    hint="1 < s < 2"
  endparam
  param bailout1
    caption="bailout 1 valut"
    default=10000.0
  endparam
  param bailout2
    caption="bailout 2 valut"
    default=0.0001
  endparam
  func fn
    caption="function 1"
    default=sin()
  endfunc
}

fhq-02 {
init:
  complex a=@parama
  z=#pixel
loop:
  z=(z^2+1)^2/(a*z*(z^2-1))
bailout:
  |z|<@bailout
default:
  title = "fhq-02"
  param parama
    caption="A valut"
    default=(1,1)
    hint="imag(a) 取值对图形影响很大 \
          real(a) not dig" 
  endparam
  param bailout
    caption="bailout valut"
    default=4.0
    hint="The valut is in (0.01 - 10.0)"
  endparam
}

palette {
init:
  complex a=flip(@powera)
  complex alpha=@alpha
  z=#pixel
loop:
  z=@fn1(a)*(z-alpha)/(z*(1-@fn2(alpha)*z))
bailout:
  |z|>@bailout
default:
  title = "palette"
  param powera
    caption="The power A"
    default=2.0
  endparam
  param alpha
    caption="Alpha Valut"
    default=(2,1)
  endparam
  param bailout
    caption="Bailout Valut"
    default=1.0
  endparam
  func fn1
    caption="Frist Function"
    default=exp()
  endfunc
  func fn2
    caption="Second Function"
    default=flip()
  endfunc
}

palette-sum {
init:
  complex a=flip(@powera)
  complex alpha=@alpha
  complex sum=0.0
  z=#pixel
loop:
  sum=sum+z
  z=@fn1(a)*(z-alpha)/(z*(1-@fn2(alpha)*z))
bailout:
  |sum|>=@bailout
default:
  title = "palette-aum"
  param powera
    caption="The power A"
    default=2.0
  endparam
  param alpha
    caption="Alpha Valut"
    default=(2,1)
  endparam
  param bailout
    caption="Bailout Valut"
    default=1.0
  endparam
  func fn1
    caption="First Function"
    default=exp()
  endfunc
  func fn2
    caption="Second Function"
    default=flip()
  endfunc
}

黎曼Function {
init:
  int n=0
  complex sum=0.0
  z=cabs(#pixel)
  s=@s+flip(z)
loop:
  n=n+1
  sum=sum+1/(n^s)
bailout:
  (@test==0&&|sum|<=@bailout)||(@test==1&&|sum|>=@bailout)
default:
  title = "黎曼 function"
  maxiter = 2000
  param test
    caption = "Bailout Test"
    default = 0
    enum = "<=" ">="
  endparam
  param bailout
    caption = "Bailout value"
    default = 1.0
  endparam
  param s
    caption="real(s)"
    default=1.23
    hint="default > 1"
  endparam
switch:
  type = "barnsleyj2"
  start = pixel
  bailout = bailout
  test = test  
}

newton2 {
init:
  complex z1=0
  complex z2=0
  complex z3=0
  complex p=0
  complex q=0
  z=#pixel
  complex zold=0.0
loop:
  zold=z
  z1=z-1
  z2=z+0.5
  z3=sqr(z)+1
  p=z1*z2*z3
  q=z2*z3+z1*z3+2*z*z1*z2
  z=((@n-1)*z^@n+@a)/(@n*z^(@n-1))-p/(q+imag(@s))  
bailout:
  |z-zold|>=@bailout
default:
  title = "newton2"
  param bailout
    caption="bailout value"
    default=0.00001
  endparam
  param n
    caption="Value N"
    default=(3,0)
  endparam
  param a
    caption="Value A"
    default=(1,0)
  endparam
  param s
    caption="Value S"
    default=(0,1.25)
  endparam
}

TEST1 {
init:
  z=#pixel
loop:
  z=-z^@power+@c
bailout:
  z<=@bailout
default:
  title = "TEST1"
  param power
    caption="power"
    default=2.0
  endparam
  param bailout
    caption="bailout"
    default=4.0
  endparam
  param c
    caption="C"
    default=0
  endparam
}

henon1 {
init:
  z=#pixel
  complex temp=0
loop:
  x=real(z)
  y=imag(z)
  temp=y+1-real(@a)*x^2+flip(imag(@a)*x)
  if @mode
    z=temp-@c
  else
    z=temp-#pixel
  endif
bailout:
  |z|<@bailout
default:
  title = "henon"
  Center=(0.250,1.0)
  Magn=0.4
  param bailout
    caption="Bailout Value"
    default=1000
  endparam
  param mode
    caption="Mode"
    default=true
  endparam
  param a
    caption="A Value"
    default=(1,1)
  endparam
  param c
    caption="C Value"
    default=(0,0)
  endparam
}

flow {
init:
  a=#pi/(30.0*@n)
  z=#pixel
loop:
  x=real(z)
  y=imag(z)
  temp=@p*x+(@b/5.0*sin(@n*@p*a)+@b*sin(@n*a))*cos(a)+\
  flip(@p*y+(@b/5.0*sin(@n*@p*a)+@b*sin(@n*a))*sin(a))
  if @mode
    z=temp-@c
  else
    z=temp-#pixel
  endif
bailout:
  (|z|<@bailout && @bailtype==0) || (|z|>@bailout && @bailtype==1)
default:
  title = "flow"
  param bailout
    caption="bailout"
    default=1E-6
  endparam
  param bailtype
    caption="bailtype"
    default=1
    enum="bailtype 1""bailtype 2"
  endparam
  param n
    caption="flows n"
    default=5
    min=2
    max=7
  endparam
  param p
    caption="P value"
    default=3
    min=1
  endparam
  param b
    caption="B value"
    default=1
  endparam
  param c
    caption="measure value C"
    default=(0,0)
  endparam
  param mode
    caption="measure Mode"
    default=true
  endparam  
}

IFSFractalTest {
init:
  z=#pixel
  complex temp=0
loop:
  x=real(z)
  y=imag(z)
  temp=y+1-real(@a)*x^2+flip(imag(@a)*x)
  if @mode
    z=temp-@c
  else
    z=temp-#pixel
  endif
bailout:
  |z|<@bailout
default:
  title = "IFS fractal  test"
  Center=(0.250,1.0)
  Magn=0.4
  param bailout
    caption="Bailout Value"
    default=1000
  endparam
  param mode
    caption="Mode"
    default=true
  endparam
  param a
    caption="A Value"
    default=(1,1)
  endparam
  param c
    caption="C Value"
    default=(0,0)
  endparam
}

斐波那 {
init:
  a=@fn1(@a)
  z=@fnz(#pixel)
loop:
  z=a*(((a+1)/2)^z-((-a+1)/2)^z)
bailout:
  (|z|<@bailout && @bailtype==0) || (|z|>@bailout && @bailtype==1)
default:
  title = "斐波那"
  magn=0.1
  param bailout
    caption="bailout"
    default=1E-6
  endparam
  param bailtype
    caption="bailtype"
    default=1
    enum="bailtype 1""bailtype 2"
  endparam
  param a
    caption="param A"
    default=5
  endparam
  func fn1
    caption="func(a)"
    default=sqrt()
  endfunc
  func fnz
    caption="Input Z"
    default=ident()
  endfunc
}

testFormula {
init:
  z=@fn4(#pixel)
loop:
  z=@fn1(z)/(@fn2(z)^@fn3(z))+@c
bailout:
  (|z|<@bailout && @bailtype==0) || (|z|>@bailout && @bailtype==1)
default:
  title = "test formula"
  Center=(0,0)
  magn=0.02
  param bailout
    caption="bailout"
    default=1E-12
  endparam
  param bailtype
    caption="bailtype"
    default=1
    enum="bailtype 1""bailtype 2"
  endparam
  param c
    caption="param c value"
    default=(0,0)
  endparam
  func fn1
    caption="function 1"
    default=ident()
  endfunc
  func fn2
    caption="function 2"
    default=ident()
  endfunc
  func fn3
    caption="power function"
    default=ident()
  endfunc
  func fn4
    caption="Input Z function"
    default=ident()
  endfunc  
}