AN EXPERIMENT IN GROWTH & FORM
Small rules. Living patterns.
Arms. Legs. Tails. One starting cell.
Change the rules. See what becomes.
Loading cell rules…STEP 0000
—living cells
—width × height
—area / reference
Preparing the experiment…
WHAT YOU’RE ACTUALLY WATCHING
A shape is a behaviour.
Each cell reads its neighbours and runs the same small neural network. The colours emerge through repeated local updates. There is no target image guiding the cells during playback.
THE RULE YOU’RE CHANGING
W = W₀ + ΔWbody + βx AₓBₓ + βy AᵧBᵧ
Your body-plan choice adds a learned adapter. The sliders add rank-one scaling changes learned on the halo; their effect on limbs and tails is exploratory.About this experiment & how it differs from the paper
This is an independently trained, smaller demonstration of the NCA + LoRA method in Hartl, Montero, Barylli, Risi & Levin, On Growth and Form, and Function (2026). It does not use the authors’ weights and is not a reproduction of their results.
- This lab: 32 × 32 cells, 12 state channels, 32 hidden units, identity + Sobel perception, a ReLU hidden layer, stochastic updates at probability 0.75, and a viability threshold of 0.1. The first four channels encode RGBA; the other eight are internal states.
- Learned here: a halo scaffold, one rank-four cross adapter, three rank-eight body-plan adapters, and two rank-one scaling adapters trained on the halo at target scales 0.7, 1.0, and 1.3 on each axis. The new body adapters are trained at their original proportions only. β = ±1 corresponds to those training endpoints, not a guarantee of the measured size.
- Body plans: the walker, tailed walker, and salamander-like form are geometric targets authored for this extension, not forms from the paper. Each uses a separately trained rank-eight adapter on the same frozen halo scaffold. Heads, limbs, and tails are visual regions, not anatomical tissue types. There are no joints, locomotion, genes, or biological development in this model.
- The paper: 67 × 67 cells, 32 channels, 96 hidden units, a shared scaffold trained on 120 emoji, rank-16 phenotype adapters and about 25,000 fitted adapters. Its extensive transfer and latent-space results are not reproduced here.
- Transfer is exploratory: applying the halo’s scale adapters to the cross or any body plan is an untrained combination. Distortion, collapse, and non-monotonic responses are possible. These are model outputs, not biological predictions.
- Damage: this model was not trained for regeneration. The paper also distinguishes morphostasis from regeneration; cutting tissue need not lead to repair.
- Implementation details: periodic Sobel perception, zero-padded viability masks, deterministic pseudorandom playback, and a smaller training budget. Playback pauses after 160 steps for a growth snapshot; Play continues the experiment. Longer runs can drift or become unstable. The reference runs the same phenotype with both scaling coefficients zero. Area counts alpha > 0.1, not a geometric target area.