Julia set fractals

Question

I wrote a program to generate Julia set fractals. The program also allows the user to enter their value of c or let the program generate a random value. Here is the code :-

import pygame, sys, math, cmath, random
from pygame.locals import *
print("Julia set fractal generator")
custom = int(input("Do you want a custom set? Yes(1); No(-1): "))
if custom == -1:
    c = complex((random.randint(-999,1000))/1000.0,(random.randint(-999,1000))/1000.0)
else:
    a = float(input("Real?: "))
    b = float(input("Imaginary?: "))
    c = complex(a,b)
lim = 4
limn = -4
mul = 0
iteration_detail = 100
screen = pygame.display.set_mode((512,512),0,32)
pygame.display.set_caption("Julia set fractal generator")
def iterate (px_i,py_i,iters):
    itnum = 1
    z = complex(((px_i-256)/512.0)*4,((py_i-256)/512.0)*4)
    while itnum <= iters:
        if z.real >= lim or z.imag >= lim or z.real <= limn or z.imag <= limn:
                break
        z = z**2 + c
        itnum += 1
return(z.real, z.imag, itnum)
def pixel_color_set (iterx, itery, iterations):
    pixel_color = (0,0,0)
    if iterx >= lim or itery >= lim or iterx <= limn or itery <= limn:
        if iterations < 2:
                pixel_color = (204,0,102)
        elif iterations == 2:
                pixel_color = (204,0,204)
        elif iterations == 3:
                pixel_color = (102,0,204)
        elif iterations ==4:
                pixel_color = (0,0,204)
        elif iterations ==5:
                pixel_color = (0,102,204)
        elif iterations ==6:
                pixel_color = (0,204,204)
        elif iterations ==7:
                pixel_color = (0,204,102)
        elif iterations ==8:
                pixel_color = (0,204,0)
        elif iterations ==9:
                pixel_color = (102,204,0)
return(pixel_color)
def draw_pixel (px, py, color):
return(screen.fill(color, ((px, py),(1, 1))))
while 1:
for event in pygame.event.get():
        if event.type == QUIT:
                pygame.quit()
                sys.exit()
        if event.type == KEYDOWN:
                if event.key == K_UP:
                        mul = 0.1
                elif event.key == K_DOWN:
                        mul = -0.1
                if event.key == K_SPACE:
                        pygame.image.save(screen, "fractal.jpg")
        if event.type == KEYUP:
                 if event.key == K_UP:
                        mul = 0
                 elif event.key == K_DOWN:
                        mul = 0
        c += mul
ypxl = 0
while ypxl < 512:
        xpxl = 0
        while xpxl < 512:
                ipxl = iterate(xpxl,ypxl,iteration_detail)
                cpxl = pixel_color_set(ipxl[0], ipxl[1], ipxl[2])
                draw_pixel(xpxl, ypxl, cpxl)
                xpxl += 1
        ypxl += 1
pygame.display.update()

The code does work but it doesn't generate fractals as expected. For example this fractal :-
z = z**2 + c Where c is equal to c = complex(-0.1, 0.651) It is supposed to look like this

But it looks like this

What is wrong in my code? Also I am unable to make a zooming mechanism... Some help there would be appreciated.

Answer 1

Changing the pixel_color_set like this gave good results.
The iterations going from 0 to iteration_detail is scaled into the range of 0 to 255.

def pixel_color_set (iterx, itery, iterations):
    pixel_color = (0,0,0)
    if iterx >= lim or itery >= lim or iterx <= limn or itery <= limn:
        RGB =int(math.sqrt(iterations) * int(255.0 / math.sqrt(iteration_detail)))
        # RGB = iterations * int(255.0/ iteration_detail)
        pixel_color = (RGB, RGB, RGB)
    return(pixel_color)

I think the one with math.sqrt looked a bit better, but try both and pick what you want.