Euclids Carpet

Euclid’s carpet is the best name I could come up with for the interference pattern that emerges when you take a series of regularly spaced shapes in a grid and grow them while keeping the center point the same.

When I first starting playing with this idea I just used circles. They usually produce quite nice results when it comes to interference patterns, and indeed it’s quite trippy (link here).

A crappy gif version

While the circles are nice, I guessed using polygons would also give nice results, so I generalised the simulation to allow for an n sided polygon instead. I found through experimentation that I enjoyed just a plain square the most – something which I wouldn’t have predicted to begin with. This can be found here, where you can also play with the number of sides using the little slider control on the right.

Something nice which you can do if you use polygons instead of a square is use a rotation to make the simulation more interesting. Here each shape rotates in the opposite direction to the one it’s next to.

Crappy gif version of the generalised carpet

The last iteration that I haven’t gotten around to yet is to use a polystar as the shape. That gives 2 separate radii to modulate, as well as a skew angle, along with the rotation that’s already being used with polygons.


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