A small script based on Hankin’s Method to generate nonperiodic plane tiling patterns. It includes a very crude method for applying colour, as well as a basic projection on a non euclidean space plus the appropriate Poincare disc. This is not an Archimedean tessellation in hyperbolic space, being just a projection of the flat Hankin tiling, .
Hi Andrei, great research! I just looked at Hankin’s wikipedia page: http://en.wikipedia.org/wiki/Ernest_Hanbury_Hankin, fascinating life story, did you get the info from his book “The Drawing of Geometric Patterns in Saracenic Art” ? Can you give example of where these patterns where used? Was it mostly carved in stone? It would be nice to see how they can be converted into three-dimensional shapes while using a similar logic (i.e. the “contact angle”.)
Arthur, that is the idea I’d like to develop for the 3d brick to get a nonperiodic pattern. It’s a fascinating old book, worth looking at, there’s been a lot of more recent research on the subject as well:
http://www.cgl.uwaterloo.ca/~csk/papers/kaplan_gi2005.pdf
http://www.mybookezzz.com/drawing-of-geometric-patterns-in-saracenic-art/
This is just some initial research I posted because a few DS10 guys were interested in the script.