Catmap

from PIL import Image
import numpy as np
import matplotlib.pyplot as plt

def mat_modexp(a,b,c):
    if b == 0:
        return np.identity(a.shape[0])
    if b % 2 == 1:
        return np.dot(a,mat_modexp(a,b-1,c)) % c
    d = mat_modexp(a,b/2,c)
    return np.dot(d,d) % c

def tN(i,n):
        s = np.shape(i)[0]
        newIm = np.zeros(np.shape(i))
        T = mat_modexp(np.matrix( [[2,1],[1,1]] ) ,n,s)

        for x in range( s ):
                for y in range( s ):
                        tC = np.dot(T, np.matrix([ [x] , [y] ]) )
                        newIm[ int(tC.A1[1]) % s ,  int(tC.A1[0]) % s ] = i[y,x]
        return newIm

img = np.asarray(Image.open('cat50.png'))

tImg = np.uint8(tN(img,150))

plt.imshow(tImg)
plt.show()