# slide rotation

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 #to save shifted pixels temporarily
fn="yourpichere.png" #must be exactly 512x512 colour png image.
xx=a.shape
yy=a.shape
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[m][i]=a[j][k+m][i]
for m in range(phalf):
s[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[m][i]
a[j+(pfull-1)-p][k+(phalf-1)-m][i]=s[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)