The second edition of Doris' remarkable book, M. C. Escher: Visions of Symmetry has been released. You have to buy it! It has a mention of this web site in it, along with the answer to the question: How many unique patterns can be made using this tiling scheme? I was the first person to solve this problem!
From 1938 to 1943, the Dutch artist M. C. Escher experimented with periodic tiling of the plane using a simple motif carved into a wooden block.
Escher rotated the block 90 degrees three times and labelled the four images thus created as 1, 2, 3 and 4.
Using a mirror image block and also two other blocks with the pattern going 'over' instead of 'under', he had 16 tiles at his disposal. The diagram below contains all 16 images as well as Escher's labelling scheme.
He would then select 4 of these blocks, arranged 2 by 2, and use this 'big tile' as a stamp to create patterns. He hand coloured some of these patterns.
To save you the trouble of carving wooden blocks, I have created an interactive application for exploring the patterns of Escher's ribbon tiles.
Steve Ogden has created a Java implementation of Ellen Gethner's colouring algorithm.
For Ellen's PhD she devised an algorithm for colouring patterns based on these tiles. Steve has implemented this in Java so that you can play it with on your computer. You must check this out, it's great!
Rui Menino has created a wonderful program for you Windows users out there. It allows you to create your own patterns and tile them in the same ways that Escher did. The site is in Portugese so here is the English google translation. I recommend this program to everybody who is interested in exploring this tiling method.
Many thanks to Doris Schattschneider, whose book M. C. Escher: Visions of Symmetry was the inspiration behind this project.