« on: August 20, 2007, 03:19:16 PM »
Knight's tour wikiKnight's tour at Wolfram MathworldKnight's Tour NotesThere Are No Magic Knight's Tours on the ChessboardOblique Quaternary Symmetry
Part 1Part 2Direct Quaternary Symmetryhttp://www.quizox.com/knightsmove.asp******************************************************************************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-FilterA 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.
« Last Edit: January 20, 2011, 09:15:38 PM by Unbeliever »
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"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 Times, May 7, 1962
God Not FoundI looked for God in my family - I didn't find Him.
I looked for God in my culture - I didn't find Him.
I looked for God in science - I found I didn't need Him.
