Research article training end-to-end differentiable, self-organising cellular automata (CA) to grow and regenerate target patterns, modeling biological morphogenesis.
Key Takeaways
Each cell holds a 16-channel state vector; Sobel filters compute local gradients forming a 48-dim perception vector fed into a shared ~8,000-parameter neural network.
Stochastic per-cell update masking (dropout at 0.5) removes reliance on global clock synchronization, making the system more plausible as a self-organising model.
The update rule is initialized to “do-nothing” via zero-weight final conv layer, then trained with gradient-based optimization to produce specific target patterns from a single seed cell.
The model learns regeneration: after damage, the CA can rebuild correct morphology, analogous to salamander limb regrowth.
Hidden state channels act as learned chemical signaling with no predefined meaning, emergent from training.
