Searching the Computational Universe for a 2-D, Three-Color Totalistic Cellular Automaton

July 28, 2016

While I was at Bentley University for the Wolfram Science Summer Program, one of our first assignments was to find an interesting two-dimensional, three-color totalistic cellular automaton (CA). These CA typically exhibit symmetrical growth and patterns. To begin, I wrote a simple line of code to generate random rule numbers to explore the computational universe for something interesting since there are billions of these type of CA. 


The first of interest is Code Number 14430587 at 500 steps with color rules 0 -> Black, 1-> Yellow, and 2-> Red.


What is particularly interesting about this CA is that it has uneven edges and irregular growth from its center. As it evolves, the edges meet then form gaps again, something not entirely unusual but definitely interesting. 


22671500 at step 500 also has odd edges. Many of the CA I examined filled the array space with patterns. This one, however, has edges that do not appear to be connected at many steps in its evolution.

These are quite beautiful to look at, but they can also be used for other interesting purposes. For example, agent based modeling sometimes uses CA to simulate the physical world. Below is a graphic for Axelrod and Hammond's ethnocentrism model generated with NetLogo. 


These types of models are not new, but there seems to be growing interest in using them to conduct research and shape public policy. If anything, they are simply cool to generate and look at.


Images produced in Mathematica 11.



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