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Knight's tours

Started by Unbeliever, August 20, 2007, 03:19:16 pm

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Unbeliever

August 20, 2007, 03:19:16 pm Last Edit: August 11, 2018, 03:59:36 pm by Unbeliever
Knight's tour wiki

Knight's Tours

Knight's Tour Challenge

Knight's tour at Wolfram Mathworld

Knight's Tours - Ben Hill, Kevin Tostado (2004)

Knight's Tour Notes

Number of possible knight's tours - OEIS

There Are No Magic Knight's Tours on the Chessboard

Modular Knight's Tours

http://danthomasson.com/cubiosities.html


Oblique Quaternary Symmetry
Part 1
Part 2

Direct Quaternary Symmetry

http://www.quizox.com/knightsmove.asp

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The vast majority of knight's tours are asymmetric or chaotic, with no discernable pattern, like this one:



Some knight's tours are symmetic, like these:



A cubic knight's tour (re-entrant)



Two similar closed (re-entrant) knight's tours with 180 degree symmetry (my own work, illustrated by Dan Thomasson):
 
 

An Image Encryption Algorithm Based on Knight's Tour and Slip Encryption-Filter

QuoteA new image encryption algorithm is proposed in the paper. Its essential idea is that, firstly, we produce a knight's tour matrix emended as slip encryption-filter template matrix; And then, we produce a knight's tour matrix again with the same size of the image waiting for encryption as a knight's tour slip matrix; Finally, we let the center of the slip encryption-filter template move along with the knight's tour slip matrix to do convolvsion operation, and achieve the cipher image. Experimental results show that the algorithm has perfert encryption effect, high encryption efficiency, simplity to achieve, huge secret key space and high security.

So, knight's tours may be applied after all, instead of pure geometry.
"Some say God is living there [in space]. I was looking around very attentively, but I did not see anyone there. I did not detect either angels or gods....I don't believe in God. I believe in man - his strength, his possibilities, his reason."
Gherman Titov, Soviet cosmonaut, in The Seattle Daily Ti