What are neural cellular automata？

Conway’s Game of Life is probably the most famous cellular automaton—a grid of cells that can either be one or zero, colored or black, alive or dead.

Neural cellular automata (NCAs) do a few things differently from classical cellular automata—for one, they are continuous where rather than a cell state being either a binary 1 or zero, it can be a decimal value in between like 0.5 or 0.2.

The first step of the NCA algorithm is the convolution—the local neighborhood part where each cell looks at its neighbors and determines its next state.

As those who might know a thing or two about neural networks might guess, much more complexity can be added by introducing what is called an activation function.

The default activation is pretty straightforward—it’s what’s called the identity function that simply returns the input x without change, as if there is no activation function at all.

In neural patterns, because the pixel value can only be between 0 and 1, the final value is clipped between 0 and 1.

The worm simulation features a funky activation function which is essentially an inverted bell curve or Gaussian, producing a really organic-looking pattern.

Activation functions can add a lot of power to the NCA algorithm—in fact, one can actually implement Conway’s Game of Life with a clever filter and activation combination.

When asked why a particular filter and activation produce a specific pattern, the honest answer is: “I have no idea.”