But Niv, what the hell is a cellular automaton?

I'm glad you asked. The simplest cellular automaton is the elementary cellular automaton. For our purposes, this is a grid of black and white cells where each cell's color is based on the closest three cells in the row above it. These three cells are called the neighborhood.

The specific way in which the neighborhood determines the color of a cell is called the rule. Below is an example of such a rule.

Source: Wolfram MathWorld

This rule says that if a neighborhood is all black, the cell below it is white. And if the neighborhood is black-black-white, then the cell below it is white. And so on.

You can make the first row of the automaton anything you want. In the game, I call this the initial state. For now, we'll leave it all white with one black cell in the center. Then, if you apply the rule all the way down, you get a pattern like this.

Source: Wolfram MathWorld

In Arcade Mode, you can explore classic automata like this, as well as totalistic automata where only the number of black and white cells in the neighborhood matters, regardless of the order. You can also try five-cell and two-step-back neighborhoods, which dramatically increase the complexity of the automata. And of course, you can cycle through every possible rule to hunt down the coolest ones.

So what's the point of all this? For one, I just think they're fun to mess with. But they're also a rich subject of mathematical study for their complex and unexpected behaviors. They sometimes generate fractals, or induce patterns out of a seemingly chaotic mess. They can engage in seemingly organic behavior that has been compared to biological life—Conway's Game of Life is a famous example. Cellular automata have also been proven to be Turing-complete, meaning they can compute the same problems as a regular computer if set up correctly and given enough time.

You can read more about cellular automata on Wolfram MathWorld.