Colossal Gardner, ch. 5

Rep-Tiles on a plane!

Sorry, wrong movie. Rep-tile was coined by mathematician Solomon Golomb to describe self-replicating tilings that can cover a plane surface. Solomon pioneered the study of these types of tilings, and developed much of the language for it.

(Image from wikipedia for a sampling of rep-tile types.)

When Gardner originally wrote this article, the link between fractals and rep-tiles wasn’t understood. Objects like the Sierpinski triangle and Sierpinski carpet are now known as self-similar fractals and are a lot of fun to make.

Hand-drawn Sierpinski triangle

Sierpinski triangle

Sierpinski carpet


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