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.
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 | # 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()
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