File:Arnold's Cat Map animation (74px).gif

#!/usr/bin/env python
#-*- coding:utf-8 -*-

import Image #needs PIL for image handling
import ImageChops
import ImageFont
import ImageDraw

# checks if two images are equal
def equal(im1, im2):
    return ImageChops.difference(im1, im2).getbbox() is None

# add a text caption to an image (adds space at the bottom)
def addCaption(im, text, pointSize):
    size = im.size
    draw = ImageDraw.Draw(im)

    textFontLocation = "/usr/share/fonts/truetype/ttf-dejavu/DejaVuSans.ttf"
    topBottomMargin = 5
    
    textFont = ImageFont.truetype(textFontLocation ,pointSize)
    textSize = draw.textsize(text, font=textFont) # the size of the text box!
    
    newImage = Image.new(im.mode,\
            (im.size[0], im.size[1]+textSize[1]+2*topBottomMargin), "white" )
    newImage.paste( im, (0,0) )
    draw = ImageDraw.Draw(newImage)
    
    textX = (newImage.size[0] / 2.0) - (textSize[0] / 2.0)
    textY = newImage.size[1] - textSize[1] - topBottomMargin
    
    draw.text((textX, textY), text, fill="black", font=textFont)
    return newImage

# add a solid border to an image
def addBorder(im, color, thickness):
    newImage = Image.new(im.mode,\
            (im.size[0]+thickness*2, im.size[1]+thickness*2), color)
    newImage.paste( im, (1,1) )
    return newImage
    
# scale an image up or down (doesn't resample, so the pixels are clear)
def scaleImage(im, factor):
    newImage = Image.new(im.mode,\
            (im.size[0]*factor, im.size[1]*factor), "white" )
    newImage.paste( im.transform((im.size[0]*factor, im.size[1]*factor),\
            Image.AFFINE,\
            (1/float(factor),0,0,0,1/float(factor),0) ),\
            (0,0) )
    return newImage
    
def saveImages(im, iteration):
    im.save("Catmap%04d.png"%iteration) #save the simple image
    
    #resize image, add border and caption
    imageLarge = scaleImage(im, 3)
    imageLarge = addBorder(imageLarge, "black", 1)
    imageLarge = addCaption(imageLarge, str(iteration), 25)
    imageLarge.save("CatmapLargeNumbered%04d.png"%iteration)

# CONTROL STARTS HERE

inFile = "aa-catmap-orig.resized.jpg" #input image

image0 = Image.open(inFile, 'r')

#crop to square if required
if image0.size[0] != image0.size[1]:
    n = min(image0.size[0], image0.size[1] )
    image0 = image0.crop((0,0,n,n))
else:
    n = image0.size[0]

imageOrig = image0.copy() # keep to original image to see when we return to it

image1 = Image.new(image0.mode, (n,n)) # temp image to copy pixels to
pixels1 = image1.load()

# BEGIN THE CAT MAPPING PROCESS

iteration = 0
saveImages(image0, iteration) # save the first image
while True:
    pixels0 = image0.load() #reload the iterated image
    
    for x in range(n):# perform the mapping
        for y in range(n):
            newX = (2*x + y) % n #find new location
            newY = (x + y) % n
            pixels1[newX, newY] = pixels0[x, y] # copy the pixel over
    
    image0 = image1.copy() #transfer back to image0 for the next iteration
    iteration += 1
    saveImages(image0, iteration) # save this iteration's image

    if equal(image0, imageOrig):
        break