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Conway's Gradient of Life
Approximate Atavising with Differentiable Automata Tuesday, May 5, 2020 · 3 min read And now, a magic trick. Before you is a 239-by-200 Conway’s Game of Life board: What happens if we start from this configuration and take a single step of the game? Here is a snapshot of the next generation: Amazing! It’s a portrait of John Conway! (Squint!) How does this trick work? (It’s not a hoax — you can try it yourself at copy.sh/life using this RLE file.) Well, let’s start with how it doesn’t work.
Reversing Life configurations exactly — the art of “atavising” — is a hard search problem, and doing it at this scale would be computationally infeasible. Surely that is hopeless… indeed, the talk I linked shares some clever algorithms that nonetheless take a full 10 minutes to find a predecessor for a tiny 10-by-10 board. (Note: This GIF is where the target image $ t $ is an all-white rectangle; my janky PyTorch gradient descent finds sparse configurations that give birth to an “overpopulated” field where nearly 90% of cells are alive.)
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