Gallian: Applications of group theory to Escher-like designs.

The three methods featured below were devised by Doug Dunham, David Witte and John Lindgren to create computer generated Escher-like graphic designs in the hyperbolic plane.

This design uses a Hamiltonian path through the symmerty group of the pattern.


Hamiltonian Circuit

This design uses a Hamiltonian path through the cosets of a subgroup (in the center of the design) of the symmerty group of the pattern.

Hamiltonian Coset

This design uses a path through the spanning tree consisting of cosets of a subgroup (in the center of the design) of the symmerty group of the pattern.

Spanning Tree

 

Video of Sargent Pepper

This video uses factor groups of the R* x R* and C* x C* to create patterns within patterns. The code was written by Josh Jacobs.

Sargent Pepper Video

Video of Day in the Life

This video was created by Josh Jacobs.

Day in the Life Video

You are the 224975 visitor of this site since February 10, 2007.