Growing Neural Cellular Automaton

Target Structure

Growth Rule

Alive threshold α 0.10

Perception radius 1 (6-neigh.)

Steps / second 6

Colony State

Step

Live cells

Match to target

Phase

growing

How it works

This is a Neural Cellular Automaton (NCA): a voxel grid where every cell holds a small state vector and runs the exact same tiny neural network to decide how to update itself, using only what its immediate neighbours are doing. There is no global controller and no cell "knows" the target shape — the pattern emerges purely from millions of identical local decisions.

for each cell c with state s_c ∈ R^n:
  p_c = perceive(neighbours of c)      // Sobel-style gradient + neighbour average
  h   = ReLU(W1 · [s_c, p_c] + b1)     // hidden layer, shared weights
  Δs  = W2 · h + b2                    // proposed update
  s_c ← s_c + Δs · stochastic_mask     // async update: only ~50% of cells fire
  alive_c ← (channel[3] of s_c) > α    // a cell "dies" if life-signal decays

Channel 0 encodes hue, channel 3 is the "alive" signal that must be sustained by living neighbours — cut off a limb (Damage) and everything downstream of it decays and can regrow, the same self-repair property real Growing-NCA models (Mordvintsev et al., 2020) trained with backpropagation exhibit. Here the weights are hand-tuned rather than trained, so growth is deterministic-ish and steered toward the picked target via a light attractor term, but the update rule, asynchronous firing and local-only perception are the real mechanism.

Alive threshold α — how much life-signal a cell needs from its neighbours to stay alive; push it up and the colony thins and can collapse.
Perception radius — 1 = 6-neighbour (face) perception, 2 = 26-neighbour (full 3×3×3) perception; wider perception grows faster and smoother.
Damage — deletes a chunk of live cells mid-growth so you can watch the local update rule regrow the missing region from its surviving edge.

Live / growing cell Grid bounds

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