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# 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
()

Diff to Previous Revision

--- revision 11 2013-08-11 03:45:36
+++ revision 12 2013-08-11 03:46:46
@@ -34,7 +34,7 @@
     zx
= x * (xb - xa) / size  + xa
     z
= zx + zy * 1j
     c
= z
-    for i in range(maxIt):
+    for i in xrange(maxIt):
         
if abs(z) > 2.0: break
         z
= z * z + c
     
return i

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