Friday, December 3, 2010

Girih tiling based on a pentagonal fractal

These girih tile drawing are loosely based on a fractal, a variant of the Koch snowflake, but pentagonal. The inside edges of the outer border of kite-shaped polygons follow a fractal. The original pentagon edges are broken three times to generate the final image. Pentagons may be used in place of the kites.

Each successive transformation of an edge into four edges was done by creating two new edges that are 72 degrees to the prior edge, and the lengths of the four new edges are 1/(2x(1+cosine(72))) of the prior edge.

Starting with a pentagon and using an angle of 72 degrees allows us to fill the interior with girih tiles. In the examples below I used a couple of scaling girih tiles.

Here is the girih line drawing I generated from the tiling. Yes, it has gaps.

Here are two more images following the same process.

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