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preserve neighborhood during random reordering

  • To: mathgroup at
  • Subject: [mg45477] preserve neighborhood during random reordering
  • From: Brent Pedersen <bpederse at>
  • Date: Fri, 9 Jan 2004 05:20:47 -0500 (EST)
  • Sender: owner-wri-mathgroup at

I have an n*n Table.  for example: 
t1 = Table[Random[Integer, {0, 10}], {k}, {k}];

I want to rearrange the elements in t1 randomly (my actual t1 has real 
data) such that for each entry t1[[i,j]] a random neighbor t1[[i+m,i+n]] 
is chosen to replace it. Once that neighbor is chosen, it can still be 
used to replace any of its other neighbors.  In the reshuffling an entry 
can replace itself. Currently I have the size of the neighborhood fixed 
at 9 cells (-1<= m,n <= 1) but eventually, I need to extend it to 25  
(-2 <= m, n <= 2), 49, etc.
I can't get my mind around how to accomplish this in a straightforward 
manner. I've tried ListCorrelate[] and RotateRight[] and combinations of 
the two.  Any suggestions would be appreciated. 

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