Thursday, March 14, 2013

Paths of Heptagons and Triangles

Here's some paths that have alternating heptagons and triangles. It's related to heptagon flowers. It looks a lot more jumbled than these flowers. This is probably due to the rotational symmetry that seems more arbitrary.

There are three local patterns that are replicated again and again with the same orientation: the large pin-wheel, the three chevrons cluster, and the propeller that has mirror symmetry.  By focusing on each of these local patterns, you can see that each pattern is arranged in a triangular lattice with a two neighbouring triangles forming pattern's fundamental region--the smallest region that can be replicated by affine transformations to recreate the whole pattern.

It's a bit mesmerising. 

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