File:Arnold's Cat Map animation (74px, labelled).gif
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Arnold's_Cat_Map_animation_(74px,_labelled).gif (76 × 100 pixels, file size: 391 KB, MIME type: image/gif, looped, 117 frames, 47 s)
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DescriptionArnold's Cat Map animation (74px, labelled).gif |
English: Animation of Arnold's cat map (with iteration numbers), using an image of cherries as the starting image. The image is 74 pixels square, and repeats after 114 iterations. Notice how the image sometimes contains superimposed cherries, many tiny cherries or a single perfectly reproduced but upside-down image. |
Date | |
Source |
Own work
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Author | Inductiveload |
Permission (Reusing this file) |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
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Other versions |
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Python source code
[edit]#!/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 = addBorder(im, "black", 1)
imageLarge = addCaption(imageLarge, str(iteration), 12)
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
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 19:23, 15 September 2010 | 76 × 100 (391 KB) | Inductiveload (talk | contribs) | {{Information |Description={{en|Animation of en:Arnold's cat map (with iteration numbers), using an image of cherries as the starting image. The image is 74 pixels square, and repeats after 114 iterations. Notice how the image sometimes contains sup |
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16 September 2010
image/gif
3180f10a5efa02163132213bb9232b5de9f2f6af
399,933 byte
46.7999999999999 second
100 pixel
76 pixel
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