FixMandelbrot {
; Mandelbrot a iteracion fija,Todos los puntos son interiores
init:
  z = 0
  int i=0
loop:
  z = z*z + #pixel
  i = i + 1
bailout:
  i <= #maxiter
;  |z|<10
default:
  title = "FixMandel"
  center = (-0.5, 0)
}

FixJulia {
; Julia a iteracion fija,Todos los puntos son interiores
init:
  z = #pixel
  int iter=0
loop:
  z = z*z + @c 
  iter=iter+1
bailout:
iter<=#maxiter
default:
  title = "FixJulia"
  center = (-0.5, 0)
  param c
    caption = "C"
    default = (-0.5,0)
  endparam
}

GenMandel {
init:
  int iter=0;
  z=pixel;
  float x=0
  float y=0
  float tmpx=0;
  float tmpy=0;
  float a0=@pa0;
  float b0=@pb0;
  float c0=@pc0;
  float d0=@pd0;
  float e0=@pe0;
  float f0=real(pixel)
  float a1=@pa1;
  float b1=@pb1;
  float c1=@pc1;
  float d1=@pd1;
  float e1=@pe1;
  float f1=imag(pixel)
loop:
  x=tmpx
  y=tmpy
  tmpx=a0*x^2+b0*y^2+c0*x*y+d0*x+e0*y+f0
  tmpy=a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1
  z=tmpx+(0,1)*tmpy
  iter=iter+1
bailout:
  |z|<@bailout
  ;iter<=#maxiter
default:
  title = "GenMandel"
  param pa0
    caption = "Real x^2"
    default = 1.0
  endparam
  param pb0
    caption = "Real y^2"
    default = -1.0
  endparam
  param pc0
    caption = "Real xy"
    default = 0.0
  endparam
  param pd0
    caption = "Real x"
    default = 0.0
  endparam
  param pe0
    caption = "Real y"
    default = 0.0
  endparam
  param pa1
    caption = "Imag x^2"
    default = 0.0
  endparam
  param pb1
    caption = "Imag y^2"
    default = 0.0
  endparam
  param pc1
    caption = "Imag xy"
    default = 2.0
  endparam
  param pd1
  caption = "Imag x"
    default = 0.0
  endparam
  param pe1
    caption = "Imag y"
    default = 0.0
  endparam
  param bailout
    caption = "BailOut"
    default = 4.0
  endparam

switch:
  type = "GenJulia"
  seed=#pixel
  pa0=pa0
  pb0=pb0
  pc0=pc0
  pd0=pd0
  pe0=pe0
  pa1=pa1
  pb1=pb1
  pc1=pc1
  pd1=pd1
  pe1=pe1
  bailout=bailout
}


GenJulia {
init:
  int iter=0;
  z=pixel;
  float x=0
  float y=0
  float tmpx=real(pixel);
  float tmpy=real(pixel);
  float a0=@pa0;
  float b0=@pb0;
  float c0=@pc0;
  float d0=@pd0;
  float e0=@pe0;
  float f0=real(@seed);
  float a1=@pa1;
  float b1=@pb1;
  float c1=@pc1;
  float d1=@pd1;
  float e1=@pe1;
  float f1=imag(@seed);
loop:
  x=real(z)
  y=imag(z)
  tmpx=a0*x^2+b0*y^2+c0*x*y+d0*x+e0*y+f0
  tmpy=a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1
  z=tmpx+(0,1)*tmpy
  iter=iter+1
bailout:
  |z|<@bailout
  ;iter<=#maxiter
default:
  title = "GenJulia"
  param seed
    caption = "seed"
    default = (-1.25,0.0)
  endparam
  param pa0
    caption = "Real x^2"
    default = 1.0
  endparam
  param pb0
    caption = "Real y^2"
    default = -1.0
  endparam
  param pc0
    caption = "Real xy"
    default = 0.0
  endparam
  param pd0
    caption = "Real x"
    default = 0.0
  endparam
  param pe0
    caption = "Real y"
    default = 0.0
  endparam
  param pa1
    caption = "Imag x^2"
    default = 0.0
  endparam
  param pb1
    caption = "Imag y^2"
    default = 0.0
  endparam
  param pc1
    caption = "Imag xy"
    default = 2.0
  endparam
  param pd1
    caption = "Imag x"
    default = 0.0
  endparam
  param pe1
    caption = "Imag y"
    default = 0.0
  endparam
  param bailout
    caption = "BailOut"
    default = 4.0
  endparam

switch:
  type = "GenMandel"
  pa0=pa0
  pb0=pb0
  pc0=pc0
  pd0=pd0
  pe0=pe0
  pf0=pf0
  pa1=pa1
  pb1=pb1
  pc1=pc1
  pd1=pd1
  pe1=pe1
  bailout=bailout
}

NewtonFnA{
; Se resuelve la ecuacion f(z)^n = c por el metodo de Newton
; Se itera z = z - (f(z)^n - c) / (f(z)^n)'
; En cada iteracion, se toma pixel por valor inicial.
; Se utiliza la expresion de derivada f'(z)=(f(z+dz)-f(z))/dz dz->0.
; Se ha utilizado un dz pequeño en la direccion del origen al pixel. 
; La ecuacion esta resuelta si f(z)^n-c=0
init:
   z = pixel
  dz = 0.00001*pixel/cabs(pixel)        
loop:
  diff1 = (@f(z+dz)^@n-@f(z)^@n)/dz   ;  (f(z)^n)'
      z = z-(@f(z)^@n-@c)/diff1       ;   
bailout:
  |@f(z)^@n - @c| >= 0.00001 && |z|<1.0e20
default:
func f
  caption="Funcion"
  hint="funcion a resolver para f(n)^n-c=0 \
        Tomar ident para newton clásico"
  default = ident()
endfunc
param n
 caption="Exponente"
 default = (3,0)
endparam
param c
 caption="Raiz"
 default = (1,0)
endparam
switch:
  type = "NewtonFnB"
  c=#pixel
  f=@f
  n=@n

} 

NewtonFnB{
init:
;$define DEBUG
  z = @c
  dz = 0.00001*pixel/cabs(pixel)
loop:
  diff = (@f(z+dz)^@n-@f(z)^@n)/dz   ;  (f(z)^n)'
     z = z-(@f(z)^@n-pixel)/diff
  print("->",z)
bailout:
  |@f(z)^@n - pixel| >= 0.00001 && |z|<1.0e20
default:
func f
  caption="Funcion"
  default = ident()
endfunc
param n
 caption="Exponente"
 default = (3,0)
endparam
param c
 caption="Valor inicial"
 default = (1,0)
endparam
switch:
  type = "NewtonFnA"
  c=#pixel
  f=@f
  n=@n
}