Yesterday I discovered Reginald Braithwaite’s wonderful essays on his site raganwald.com. One of the first ones I read, Why Recursive Data Structures? presents “an uncommon, but particularly delightful way” to rotate a square. This is a modified version, with sliding in only 2 directions.
(It’s a 31MB GIF, may take a while to play smoothly)



Q. When is the rotation?!

written in Sage cython.

PicRotate.pyx:

import numpy as np
cimport numpy as np
from scipy import misc

cpdef OK():
    cdef int i,j,m,n,p,k,c,t,xx,yy,temp,pw,pfull,phalf
    cdef np.ndarray[np.uint8_t, ndim=3] a
    cdef int s[2][260][3] #to save shifted pixels temporarily
    fn="yourpichere.png" #must be exactly 512x512 colour png image.
    a=misc.imread(fn)
    xx=a.shape[0] 
    yy=a.shape[1]
    c=0
    t=30
    for i in range(t):
        misc.imsave('%05d.png' % c,a)
        c+=1
    if t>1: t-=1
    for j in range(0,xx,2):
        for k in range(0,yy,2):
            for i in range(3):
                temp=a[j][k][i]
                a[j][k][i]=a[j+1][k][i]
                a[j+1][k][i]=a[j+1][k+1][i]
                a[j+1][k+1][i]=a[j][k+1][i]
                a[j][k+1][i]=temp
    for i in range(t):
        misc.imsave('%05d.png' % c,a)
        c+=1
    if t>1: t-=1
    for pw in range(2,10):
        pfull=2**pw
        phalf=pfull/2
        for p in range(phalf): 
            for i in range(3):
                for j in range(0,xx,pfull):
                    for k in range(0,yy,pfull):
                        for m in range(phalf):
                            s[0][m][i]=a[j][k+m][i]
                        for m in range(phalf):
                            s[1][m][i]=a[j+(pfull-1)][k+(pfull-1)-m][i]
                        for m in range(pfull-1-p): 
                            for n in range(phalf): #slide
                                a[j+m][k+n][i]=a[j+m+1][k+n][i]
                                a[j+(pfull-1)-m][k+(pfull-1)-n][i]=a[j+(pfull-2)-m][k+(pfull-1)-n][i]
                        for m in range(phalf):
                            a[j+p][k+phalf+m][i]=s[0][m][i]
                            a[j+(pfull-1)-p][k+(phalf-1)-m][i]=s[1][m][i]
                            
            for i in range(t):
                misc.imsave('%05d.png' % c,a)
                c+=1
            if t>1: t-=1
            print fn
    for i in range(30):
        misc.imsave('%05d.png' % c,a)
        c+=1

to run it, in the Sage command line type “%attach PicRotate.pyx” then “OK()”.

(Jan 2017)