Differentiable morphogenesis · WebGPU

Teach one cell to become an organism.

Synaptic unrolls a neural cellular automaton through time, trains its shared local rule, and continuously runs what it has learned in the live growth and regeneration simulation below.

3 × 3 perception identity · Sobel x · Sobel y
zero padded

48 → 128 → 16 shared pointwise MLP
ReLU activation

Residual update 50% stochastic fire mask
random 64–96-step tape

Life mask pre + post alpha tests
damage sample pool

Training target

Flower · 24 × 24 premultiplied RGBA

Upload image

Live organism

Responsive live grid · latest learned rule · click or drag to damage after regeneration

Phase 1 · growth · 0%

01 Growth seed → target · repeated quality checks 0% active

02 Stability retained states · repeated quality checks 0% waiting

03 Regeneration 96 damaged batches · ≥90% strict passes 0% waiting

iteration0

loss—

rollout—

train step—

damaged samples0

auto resets0

initializing WebGPU…

How it works

One local rule, learned through time.

Every cell runs the same tiny neural network. Repeating that local rule turns one living seed into a target that can persist and eventually repair itself.

01 · CELL RULE

See the neighborhood, then predict a change.

A cell stores premultiplied RGBA plus twelve learned hidden channels. Fixed, zero-padded identity and Sobel x/y filters read each channel's 3 × 3 neighborhood. The resulting 48 values enter a shared pointwise network; a 50% fire mask applies its residual update. Pre- and post-update alpha masks keep growth attached to living cells and clear dead hidden state.

16 channels × 3 filters → 48 → 128 ReLU → 16 Δ

02 · LEARNING OVER TIME

Learn a process, not a snapshot.

Each lesson lets the organism evolve for a random 64–96 generations. Synaptic scores its final sixteen states, rewarding accurate color, crisp edges, the right living shape, and stable internal values. Scoring a sequence prevents the organism from resembling the target for only one lucky moment.

L1 counts every difference by its size. L2 squares differences, giving larger mistakes extra weight. Together they provide steady correction and strong pressure on obvious errors. They contribute to the loss shown above: zero is an exact match, and lower is better.

Synaptic traces that feedback backward through the recorded generations—backpropagation through time—then Adam makes a measured update to the shared rule.

grow → score the final 16 states → trace mistakes → adjust the rule

03 · SAMPLE POOL

Practice growth, persistence, and repair.

Evolved grids return to persistent pool slots and become later starting states. This experiment retains 512 histories while keeping the GPU batch at eight. The worst selected sample is replaced by a fresh seed, while healthy samples eventually receive round or elongated target-anchored cuts and must recover the complete target. This widens the target's basin of attraction: more partial, old, and differently damaged states naturally evolve back toward it.

seed + retained + damaged states → target attractor

An evidence-based curriculum

A phase advances only when a rolling set of recent trials is consistently good, including the weakest example in each batch. The check balances image accuracy, living-cell count, and target coverage; later phases must also preserve earlier skills. If progress stalls for sixteen full windows, Synaptic keeps the learned rule, refreshes its practice states, clears learning momentum, and briefly raises the learning rate.

01 · Growth: Fresh seed → target. No pool or damage. 16 observations at 92% confidence; relative loss ≤ .08, target coverage ≥70%, and living count 60–160%.
02 · Stability: Retained pool states → target. 32 observations at 92% confidence; relative loss ≤ .06, target coverage ≥80%, and living count 70–145%.
03 · Regeneration: Target-anchored cuts → target. 96 damaged batches at 97% confidence with ≥90% strict passes; relative loss ≤ .04, target coverage ≥90%, living count 80–125%, and damage ramps 50–100%.