Growing Neural Cellular Automata: Differentiable Models That Self-Assemble and Regenerate

Researchers at Distill applied differentiable programming to cellular automata, training tiny per-cell neural networks to grow target images from a single seed cell. Each cell holds a 16-dimensional state vector — three RGB channels, an alpha channel marking living tissue, and twelve hidden channels acting as learned chemical signals. The update rule is a 3x3 convolution followed by per-cell operations, identical across the grid, mirroring how every cell in an organism shares one genome but differentiates through local signaling.

The team trained three variants with progressively stronger stability properties. Growing models reliably produce the pattern but often destabilize afterward. Persistent models, trained to hold the pattern across longer time horizons, unexpectedly develop partial regenerative behavior as a side effect. Regenerating models, which see damaged states during training, recover robustly from cuts and erasures, rebuilding the target shape from whatever cells survive.

The work positions CAs as a tractable in-silico analogue for morphogenesis, the still-unsolved question of how cell collectives know what to build and when to stop. By making the local rules differentiable, the authors turn a biological mystery into a gradient-descent problem, and hint at engineering applications — self-repairing structures, regenerative medicine — that depend on cracking that same code.