#MathArtChallenge Day 59: Cellular Automata

6 different iterations of random assignment automata

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

Materials needed: grid (can be home made!) paper, pencil/pen.
Math concepts you could explore with this challenge: Probability, randomness, expected value

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!

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments! 

1.) Make sense of problems and persevere in solving them. After attempting a few of these, see if you can design a starting row and predict the design or pattern that results.

3.) Construct viable arguments and critique the reasoning of others. Is it possible to design one of these that will end either all black or all white?

Author: Ms. P

Math Teacher in Minneapolis, MN.

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