Recovering the rule behind a Lenia body

Here the search receives a complete body from the dataset as its initial field. The search must find a rule that keeps that field coherent, active, and topologically similar during the recorded rollout. It can now test how to sustain the anatomy without also having to discover how to grow it.

Orbium lets us ask how much a mature body reveals when we already know the kind of rule that made it. We supplied its update law, kernel, growth function, and starting cells, then hid three numerical parameters: the interaction radius R, growth center m, and growth width s. Each candidate develops from those same starting cells and is compared with the reference body at step 600.

The reconstructions raise a question about the whole collection: how many different rules can fit a similar body? We represent each body by its measured phenotype and call the set of compatible rules a fiber. If that set is broad, choosing a measured form still leaves considerable freedom in the dynamics that produce it.

Retrieving a nearby rule gives the search a starting point; running it reveals whether that proposal produces the requested measurements. Earlier tests examined both parts: whether proposed rules produce stable bodies, and whether simulation-guided refinement improves their match across several targets.

A body that matches the requested shape may still move differently. To examine that gap, we measured six behaviors in 8,174 creatures and reduced them to principal axes. The first axis is dominated by speed, path length, displacement, and center velocity, so we call it locomotion. The second is dominated by energy and temporal variance, so we call it activity. Together they account for 87.2% of the behavioral variation.

If many trajectories finish in the same region, it is tempting to picture development as rolling downhill toward it. We tested that picture by fitting a potential surface to the endpoints and comparing its downhill direction with the observed motion. The alignment was weak. In a separate test, five of eight genotypes became more dispersed after their starting conditions were perturbed. Frequent endpoints therefore did not supply the restoring dynamics a compiler would need to rely on.

The two searches solve different parts of the problem, maintaining a supplied field and recovering parameters within a known family. None yet discovers both a compact seed and a rule that reliably grows an arbitrary requested body.

The ledger records the source for every number, specimen, replay, and reused schematic. SHA-256 identifies the exact bytes. The June files do not contain the revision that produced those historical results; the September case-study entries include their exact configs and media.