Fractais de Newton Versão 2026.04.27 f(z)=z^5 -1

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# Fractais de Newton
# v. 2026.04.27
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#
#  Carlos Paulo A. Freitas (cpaulofonline@gmail.com)
#  https://zonaexacta.blogspot.com
#  https://sites.google.com/view/cpaulof-prog-calc
#
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import kandinsky,math
LARGURA = 320
ALTURA = 222
# Area a percorrer
X_MIN = -2.0
X_MAX = 2.0
deltaX=(X_MAX-X_MIN)/(LARGURA-1)
Y_MIN =-ALTURA/2*(X_MAX-X_MIN)/LARGURA
Y_MAX = ALTURA/2*(X_MAX-X_MIN)/LARGURA
deltaY=(Y_MAX-Y_MIN)/(ALTURA-1)
M = 45 # maximo de iteracoes
E = 1E-14# E (epsilon)= margem de erro ...vou usar a mesma para tudo

#Cores: vou deixar 9 cores
F=255
cores = [
 [0,0,0], #0 preto
 [F,F,F], #1 branco
 [F,0,0], #2 vermelho
 [0,F,0], #3 verde
 [0,0,F], #4 azul
 [F,0,F], #5 violeta
 [F,F,0], #6 vermelho+verde=
 [0,F,F], #7
 [204,153,0] #8
]
N_COLORS=9
# Funcao complexa
def f(z):
    return z*z*z*z*z-1
    
# Derivada
def df(z):
    return 5*z*z*z*z
    
def FractalNewton():
  # desenhar o fractal
  nzeros=0 #numero de zeros que ja apareceram
  zero=[]  #lista dos zeros que ja apareceram
  zero_=-1 #posicao do zero actual na lista
  for k in range(LARGURA):
     C=0 #nivel de escuridao
     x = X_MIN + k*deltaX
     oldx = x - deltaX
     for l in range(ALTURA):
          y = Y_MIN+(ALTURA-l)*deltaY
          z = complex(x, y)
          oldz = complex(oldx, y+deltaY)
          m=0
          print("(",k,",",l,"), nzeros=",nzeros)
          while(m<M and (abs(z-oldz))>=E):
            oldz=z
            z = z - f(z) / df(z) # Formula recursiva do metodo de Newton
            if (abs(z-oldz) < E):    # Testar se z ja a variar pouco
                if nzeros==0:
                    zero_=0
                    zero.append(z)
                    nzeros = nzeros + 1
                    print("Numero de zeros=",nzeros,":",z)
                else: 
                    estanalista=False
                    for j in range(nzeros):
                        estanalista=(abs(z-zero[j])<1E-7)
                        if estanalista:
                            zero_=j
                            break
                    if( not estanalista ):
                        zero.append(z)
                        zero_=nzeros
                        nzeros = nzeros + 1
                        print("Numero de zeros=",nzeros,":",z)
                        break
                cor=zero_
                if (zero_==0):
                  cor=6 #amarelo
                elif zero_==1:
                  cor=4 #azul
                elif zero_==2:
                  cor=2 #vermelho
                elif zero_==4:
                  cor=5
                                      
                C=m/(M+0.0);C=1-math.sin(C*math.pi/2);
                col = kandinsky.color(int(C*cores[cor][0]),int(C*cores[cor][1]),int(C*cores[cor][2]))
                kandinsky.set_pixel(k, l, col)                
            else:
              col = kandinsky.color(cores[0][0],cores[0][1],cores[0][2])
              kandinsky.set_pixel(k, l, col)                
            m=m+1

FractalNewton()