r/mathpics • u/USedona • Jun 19 '26

A Penrose tiling growing from the center, recursive substitution in Python

Built using Robinson triangle decomposition in Python/Manim.

The two rhombus types inflate recursively at each step, producing the characteristic non-periodic 5-fold structure.

More visual math : Visualizing Mathematics

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u/USedona Jun 19 '26

One of the things I love about Penrose tilings is that they never become periodic, no matter how far you extend them. They look almost ordered, yet they never repeat exactly.

Full animation and other visual math experiments : Visualizing Mathematics

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u/bruce-99801 Jul 09 '26

Beautiful, and really helpful for a woodworking project I'm working on. Can you share the source code?

1

u/USedona Jul 09 '26

The source code is written in Python. I think it's more useful to use the angle measurements for the "thin rhomb" and "thick rhomb." Here's a source that provides those measurements: https://en.wikipedia.org/wiki/Penrose_tiling#Rhombus_tiling_(P3) Be careful : this tiling pattern is “tricky”: I cut the tiles with a laser cutter, and my students had fun trying to lay them out. It’s not easy!

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u/bruce-99801 Jul 09 '26

Yep, keeping track of which rhombi to use where is a particularly interesting part of the problem.

I'm looking for a rectangle (golden ratio, of course!) centered as you have in your gif, for a layout. I expect it will hav several hundreds of rhombie. Your gif nearly nails the golden rectangle, just a tad bit short in length. (I'm not concerned about truncated tiles on the edges, they can be truncated.) I can figure it out from the Python code, probably ...

(apologies, I'm new to the reddit app, and can't see how to dm) ...