Writing

Recovering the rule behind a Lenia body

One observed frame of Orbium was enough for a search to recover its rule close to the native values, and the recovered rule keeps the body coherent well past the frame it was fitted to.

Orbium under its native rule at step 1,200. — Orbium at step 1,200 under the native rule (left) and the recovered rule (right).

Orbium under the recovered rule at step 1,200. — Orbium at step 1,200 under the native rule (left) and the recovered rule (right).

Cells that wait their turn form islands in self-sorting arrays

Cells of one sorting rule gather into islands because they wait for nearby cells to sort; islands outlast the sort when one kind keeps overtaking its equals.

Three arrays sorting over time, with cells of two rules coloured orange and blue. Where one rule waits, same-coloured cells gather into long vertical islands; where neither waits, the colours stay mixed.

Proof search with a missing tactic

We block one tactic from a successful Lean proof search and rerun it under the same budget to see whether the prover still reaches the theorem by another route.