Recursive Mandelbrot Generation (Python recipe) This program recursively generates a Mandelbrot set using Python and PyGame. The size of the window must be a power of two or you will get rendering errors in the final image. It was written as an exercise in recursion, primarily to further my own understanding of that. Created by Bill Pickett on S…

mandelbrot_recursion.py

# Recursively draw the Mandelbrot set
# Dependencies: Python 2.7.5, PyGame 1.9.1

import pygame
from pygame.locals import QUIT
from sys import exit

# size must be a power of 2 or you will get rounding errors in the image
# E.g. 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, ...
size = 512

pygame.init()
surface = pygame.display.set_mode((size, size), 0, 32)

# Mandelbrot drawing area
xa = -2.0
xb = 1.0
ya = -1.5
yb = 1.5

# maximum iterations
maxIt = 256

def pump():
    # pump the event queue so the window is responsive, exit if signaled
    for event in pygame.event.get():
        if event.type == QUIT:
            pygame.quit()
            exit()

def point(x, y):
    # get the escape value of a specific coordinate in the Mandelbrot set
    zy = y * (yb - ya) / size  + ya
    zx = x * (xb - xa) / size  + xa
    z = zx + zy * 1j
    c = z
    for i in xrange(maxIt):
        if abs(z) > 2.0: break
        z = z * z + c
    return i

def col(c):
    # return a color variable computed from a escape value
    return (c % 4 * 64, c % 8 * 32, c % 16 * 16)

def mandel(x, y, i_size):
    p1 = point(x, y)
    half = i_size / 2
    # if half > 1 then there are still possible sub-divisions
    if half > 1:
        # if all the pixels around the square are the same then it can just
        # be filled instead of sub-divided - test the square
        test = False
        for i in xrange(i_size):
            t1 = point(x, y + i)
            t2 = point(x + i, y)
            t3 = point(x + i_size, y + i)
            t4 = point(x + i, y + i_size)
            if (p1 != t1 or p1 != t2 or p1 !=t3 or p1 != t4):
                test = True
                break
        if test:
            # The colors all around the square are not equal so sub-divide
            mandel(x, y, half)
            mandel(x + half, y, half)
            mandel(x + half, y + half, half)
            mandel(x, y + half, half)
        else:
            # This is a base case, all square border points are same color
            # fill area and return back up the stack
            surface.fill(col(p1), (x, y, i_size, i_size))
    else:
        # This is a base case, a 2x2 block. Plot the four pixels
        # and return back up the stack
        p2 = point(x + i_size - 1, y)
        p3 = point(x + i_size - 1, y + i_size - 1)
        p4 = point(x, y + i_size - 1)
        surface.lock()
        surface.set_at((x, y), col(p1))
        surface.set_at((x + i_size - 1, y), col(p2))
        surface.set_at((x + i_size - 1, y + i_size - 1), col(p3))
        surface.set_at((x, y + i_size - 1), col(p4))
        surface.unlock()

    pygame.display.update()
    pump()

# calculate the image
mandel(0, 0, size)

# Wait for user to click close widget on window
while True:
    pump()