Differentiable morphogenesis · WebGPU

Teach one cell to become an organism.

Synaptic unrolls a neural cellular automaton through time, trains its shared local rule with backpropagation, then streams the same weights into Automata for a live growth and regeneration simulation.

training in browser

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

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Automata inference

Responsive live grid · exact artifact handoff · 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—

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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 · TRAINING TAPE

Judge an unfolding process, not one frame.

Each optimizer update records a random 64–96-generation trajectory. The same target is scored at each of its final sixteen states, so the organism must stay correct instead of briefly passing through the image. Its loss is the mean squared difference between predicted and target RGBA across every pixel and batch sample: zero is an exact match, and lower is better.

BPTT (backpropagation through time) carries those errors backward through the entire tape. Adam (adaptive moment estimation) then turns the resulting gradients into weight updates using momentum and an adaptive step size for each weight.

rollout → MSE loss → BPTT gradients → Adam update

03 · SAMPLE POOL

Practice growth, persistence, and repair.

Evolved grids return to persistent pool slots and become later starting states. The worst sample is replaced by a fresh seed, while healthy samples are eventually cut and asked to recover the complete target. This widens the target's basin of attraction: more partial, old, and damaged states naturally evolve back toward it.

seed + retained + damaged states → target attractor

An evidence-based curriculum

A phase advances only after a full rolling evidence window meets its confidence and pass-rate bar. The score uses the worst sample in each batch—not its average—and combines target-normalized image loss, living-cell bounds, and coverage of visible target cells. Every later phase must also preserve the earlier skills.

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%.