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.

Answer 2

You could also use your original coloration algorithm if you use the remainder of division by 10 of the iteration count to decide the color. But then you have to check first for the maximum count to have the inside always black. Or encode the maximum count by setting the iteration number to -1 after the computation loop, this is easier to check in the coloration method.

Answer 3

Whats wrong with my code ?

Nothing, you have good image, but you want different image. To make new image change the drawing algorithm. The image you want to make is : Julia set for fc(z)=z*z + c and c=-0.1+0.651. Made using DEM/J

It is made with distance estimation not with escape time as in your program

So simply change the algorithm

HTH