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  KNOT THEORY : A new simplification algorithm for knot diagrams


I have discovered a very simple algorithm that quickly simplifies any given knot or link diagram, bringing it to a minimal crossing number status. In particular, the algorithm completely untangles any diagram of the unknot. I have written a code implementing this algorithm. Follow the links below to read the theorical explanation of the algorithm, to download the installation package for the software implementing it, and to see pictures (in pdf format) produced by the software and illustrating the performance of the algorithm on many well-known and hard knot diagrams.

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For more information:
adolfo@zanellati.it
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Download Explanation of the algorithm
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Download Knotsolver installation package (for Windows):.    

Simplification of famous diagrams:

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Satellite_knot of Haken.    
Download Satellite_knot of Haken.    
 
Haken gordian knot.    
Download Nodo gordiano di Haken italiano.    
Download Haken gordian knot english.    
 
 
Satellite_knot of Joel Hass.    
Download Satellite_knot of Joel Hass.    
 
Goeritz.    
Download Goeritz.    
 
Culprit.    
Download Culprit.    
 
Thistlethwaite.    
Download Thistlethwaite.    
 
32_crossings_diagram.    
Download 32_crossings_diagram.    
 
 © Adolfo Zanellati - email: adolfo@zanellati.it