// Bad Behavior Start $txt['permissionname_badbehavior_goodgroup'] = 'Bad Behavior Whitelist Group'; $txt['permissionhelp_badbehavior_goodgroup'] = 'This option will make a member group exempt from all Bad Behavior tests.'; // Bad Behavior End // Begin Auto Embed Media Pro Text Strings $txt['mediapro_admin'] = 'Simple Audio Video Embedder'; $txt['mediapro_settings'] = 'Settings'; $txt['mediapro_save_settings'] = 'Save Settings'; $txt['mediapro_err_cache'] = 'Cache folder not writable must fix for performance!'; // END Auto Embed Media Pro Text Strings $txt['botscout_mail_subject'] = 'Bot Attempt Stopped'; $txt['botscout_mail_body'] = 'A bot tried to register, but was stopped from doing so.' . "\n\n" . 'Bot Name: %s' . "\n" . 'Bot Email: %s' . "\n" . 'IP Address: %s'; Knight's tours

Author Topic: Knight's tours  (Read 1517 times)


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Knight's tours
« on: August 20, 2007, 03:19:16 PM »
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


Oblique Quaternary Symmetry
Part 1
Part 2

Direct Quaternary Symmetry



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

A 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: August 11, 2018, 03:59:36 PM by Unbeliever »
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