More Wiggling Polygons

Lately, I've been wiggling shapes together to try to make interesting tessellations.


I have to say every time I make a foray into this sort of design, I have to stop an appreciate 500 year old tile artists who managed to work out these patterns without computer assisted drawing (although, they do fudge shapes away from strict geometric polygons).


What typically happens is that I start in on a design that clicks into place on a local level but once I start to extend the repeats out -- or try rotating the whole pattern 120 degrees instead of 90 -- there's a fractional repeat that starts adding additional recursive shapes.


Theoretically, one could get around the difficulties of using both squares and triangles by designing a pattern with twelve-fold symmetry).


Looking at books on design, it seems the best strategy is to arrange squares and triangles and stars along radial guidelines and then wait for patterns to snap (mostly) into place.


Five-fold symmetry, as I've noted before, is very hard to tessalate unless one folds the two-dimensions of the workspace into three dimensions.  My intuition tells me that folding a pattern of ten stars into a regularly repeating pattern is somehow part of the same property of our universe that means you have to fold sound somehow if you want to make seven octaves and twelve fifths a unison.