#MathArtChallenge Day 59: Cellular Automata

The Challenge: Using rules from the “above row”, create a new row below.

Materials needed: grid (can be home made!) paper, pencil/pen.


To make, create a set of “rules” for yourself. Here, you can see that I assigned each pair of adjacent squares a color for the square below. So in the top left, BlackBlack(BB) yields Black, BW yields white, WB yields B, and WW yields W. I then just followed that pattern down.

For all 6 of my images, I started with the same top row (arbitrarily chosen by flipping coins)


But I applied all six of the “4 choose 2” rule options where there were 2 black and 2 white squares resulting. You could definitely play with a 3-1 result, too.

I found it delightful to see the different results.

You could also create a full rectangle by using the far left and far right squares (imagine taking the left/right sides and folding into a cylinder), or you could do this on a hexagon grid, too!

Would love to see anything you create!

And here’s where I got the idea. Thanks, Bowman!

Author: Annie Perkins

Math Teacher in Minneapolis, MN.

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