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Sierpinski’s Carpet Animation

By Dibson on 2009 November 19

A few weeks ago I wrote a little script (code below the fold) to generate the frames of the following animation. It’s an animation of different iterations of Sierpinski’s Carpet.

7 Iterations of the Carpet

7 Iterations of the Carpet

To generate the carpet, take a square. Divide it into nine squares (3×3) and remove the center one. Then, for each of the remaining 8 squares, repeat ad infinitum.

If you get bored doing it an infinite number of times, take a break and eat Sierpinski’s Cookie.

The Code – SierpinskisCarpenter.py

Sorry for the crappy box this is in. Copy and paste for reading.

  1.  
  2. #!/usr/bin/python
  3.  
  4. #
  5. # SierpinskisCarpenter.py
  6. #
  7. # Author: Dibson T Hoffweiler <dibson@hoffweiler.com>
  8. # WWW:    http://www.dibson.net/
  9. #
  10. #             DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
  11. #                     Version 2, December 2004
  12. #
  13. #  Everyone is permitted to copy and distribute verbatim or modified
  14. #  copies of this license document, and changing it is allowed as long
  15. #  as the name is changed.
  16. #
  17. #             DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
  18. #    TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
  19. #
  20. #   0. You just DO WHAT THE FUCK YOU WANT TO.
  21. #
  22.  
  23. import Image
  24.  
  25. class SierpinskisCarpenter:
  26.    
  27.     def __init__(self):
  28.         """ Prepare the Carpenter """
  29.         self.color = (0, 0, 255)
  30.  
  31.     def getCounter(self):
  32.         """ Return current counter value, increment it. """
  33.         c = self.counter
  34.         self.counter += 1
  35.         return c
  36.  
  37.     def getFrameFilename(self):
  38.         """ Return filename for next frame. """
  39.         return "carpet-frame-%02d-%06d.gif" % (self.itr_start, self.getCounter())
  40.  
  41.     def getCarpetImage(self, itr, size, init=True):
  42.         """ Return an image object of Sierpinski’s Carpet
  43.  
  44.            itr – int – how many iterations deep to go
  45.            size – int – width of carpet in pixels
  46.            init – bool – if True, clear counters – must set False when recursing! (default True)
  47.        """
  48.  
  49.         if (init):
  50.             # Prepare to lay the carpet out
  51.             self.counter = 0
  52.        
  53.         if (0 == itr):
  54.             # No need to iterate, return the part
  55.             part = Image.new("RGB", (size, size), self.color)
  56.             return part
  57.         else:
  58.             # Get smaller carpet, and paste it in 8 times
  59.  
  60.             third = size / 3
  61.  
  62.             partSmall = self.getCarpetImage(itr – 1, third, False)
  63.            
  64.             im = Image.new("RGB", (size, size), (255, 255, 255))
  65.  
  66.             # top left
  67.             tl_start = (0, 0)
  68.             im.paste(partSmall, tl_start)
  69.  
  70.             # top center
  71.             tc_start = (third, 0)
  72.             im.paste(partSmall, tc_start)
  73.  
  74.             # top right
  75.             tr_start = (2 * third, 0)
  76.             im.paste(partSmall, tr_start)
  77.  
  78.             # middle right
  79.             mr_start = (2 * third, third)
  80.             im.paste(partSmall, mr_start)
  81.  
  82.             # bottom right
  83.             br_start = (2 * third, 2 * third)
  84.             im.paste(partSmall, br_start)
  85.  
  86.             # bottom center
  87.             bc_start = (third, 2 * third)
  88.             im.paste(partSmall, bc_start)
  89.  
  90.             # bottom left
  91.             bl_start = (0, 2 * third)
  92.             im.paste(partSmall, bl_start)
  93.  
  94.             # middle left
  95.             ml_start = (0, third)
  96.             im.paste(partSmall, ml_start)
  97.  
  98.             return im
  99.  
  100.     def animateCarpet(self, itr, size, start=None):
  101.         """ A recursive function to generate an animation of drawing Sierpinski’s Carpet.
  102.        
  103.        - itr – int – how many iterations to do
  104.        - size – int – image size will be a square with lengths this many pixels
  105.        - start – 2dim tuple – top left corner of carpet to draw
  106.  
  107.        Example:
  108.  
  109.          sc = SierpinskisCarpenter()
  110.          itr = 3
  111.          size = (3 ** itr, 3 ** itr)
  112.          im = sc.animateCarpet(itr, size)
  113.          im.show()
  114.  
  115.        """
  116.  
  117.         if (None == start):
  118.             # Init the animation
  119.             start = (0,0)
  120.             self.counter = 0
  121.             self.im = Image.new("RGB", (size, size), (255, 255, 255))
  122.             self.itr_start = itr
  123.             self.im.save(self.getFrameFilename())
  124.  
  125.         # tab for clean debug output
  126.         tab = "\t" * itr
  127.  
  128.         #print tab + "MAKE CARPET ITR %s" % (itr)
  129.         #print "%sStart %s" % (tab, start)
  130.  
  131.         if (0 == itr):
  132.             # LAST ITERATION – PAINT IT!
  133.             #print "%sPAINTING: Start %s" % (tab, start)
  134.             self.im.paste(self.color, (start[0], start[1], start[0] + size, start[1] + size))
  135.             self.im.save(self.getFrameFilename())
  136.         else:
  137.             # NEED TO ITERATE, DO ALL 8 SQUARES
  138.  
  139.             third = size / 3
  140.    
  141.             # top left
  142.             tl_start = (start[0], start[1])
  143.             self.im = self.animateCarpet(itr-1, size/3, tl_start)
  144.    
  145.             # top center
  146.             tc_start = (start[0] + third, start[1])
  147.             self.im = self.animateCarpet(itr-1, size/3, tc_start)
  148.    
  149.             # top right
  150.             tr_start = (start[0] + 2 * third, start[1])
  151.             self.im = self.animateCarpet(itr-1, size/3, tr_start)
  152.    
  153.             # middle right
  154.             mr_start = (start[0] + 2 * third, start[1] + third)
  155.             self.im = self.animateCarpet(itr-1, size/3, mr_start)
  156.  
  157.             # bottom right
  158.             br_start = (start[0] + 2 * third, start[1] + 2 * third)
  159.             self.im = self.animateCarpet(itr-1, size/3, br_start)
  160.  
  161.             # bottom center
  162.             bc_start = (start[0] + third, start[1] + 2 * third)
  163.             self.im = self.animateCarpet(itr-1, size/3, bc_start)
  164.    
  165.             # bottom left
  166.             bl_start = (start[0], start[1] + 2 * third)
  167.             self.im = self.animateCarpet(itr-1, size/3, bl_start)
  168.    
  169.             # middle left
  170.             ml_start = (start[0], start[1] + third)
  171.             self.im = self.animateCarpet(itr-1, size/3, ml_start)
  172.    
  173.         return self.im
  174.  
  175. cm = SierpinskisCarpenter()
  176.  
  177. # EXAMPLE: saves 6 iterations of Sierpinski’s Carpet
  178. #topItr = 6
  179. #size = 3 ** topItr
  180. #for itr in range(topItr+1):
  181. #    im = cm.getCarpetImage(itr, size)
  182. #    im.save("carpet-%spx-%s.gif" % (size, itr))
  183.  
  184. # EXAMPLE: dumps out frames for drawing out carpet
  185. #cm.animateCarpet(3, 27)
  186.  
  187.  

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