Knight Life

The Game of Life is the most famous cellular automaton ever devised. The rules are dead simple, and the expressive power of the game is enormous. People have used it as a metaphor for a whole host of other phenomena, from evolution to the fundamental laws of the universe. However, I have long had the sense that Life has a hidden weakness that makes its results far more of a special case than people tend to imagine. That weakness is its neighborhood.

What I mean by the neighborhood is the fact that each cell in the game updates according to the cells that sit around it, both adjacent and diagonal. The combination of a small neighbor set coupled with more than one kind of physical relationship packs a ton of expressive power into a simple system. However, this comes at the cost of making the Game of Life massively anisotropic. Change the relationship between cells just a tiny bit, I guessed, and the cool patterns would disappear. If this idea was right, it suggested that the Game of Life, and other automata like it, have a lot less to do with natural organisms, or the universe, than first appears.

To test my theory, I decided to see what would happen to the Game of Life if you played it with a different neighborhood–one with the same number of neighbors, but treating all neighbors exactly the same way. To do this, I replaced the standard set of neighbor relations with the set of knight-moves.

What was the result? You can see for yourself below.

As expected, the clever compact patterns from Conway’s original game disappear. However, ironically, what you gain is something that looks a lot more like what you might find under a microscope.

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