Specter Labs emblemSPECTER LABS

What recurs
across different
systems?

We investigate whether different kinds of systems share principles of organization: how a body takes shape, how a collective finds a solution, how a pattern survives disruption. We build experiments in living systems and computational worlds to uncover those principles.

Explore the investigations ↘
Quadrium-derived Lenia
“We realised that my equations describing molecular evolution were similar – and some almost identical – to those left over on the blackboard by Hermann Haken. Could it be that things as different as laser modes and DNA resemble one another so closely in their dynamic behaviour?”

— Manfred Eigen, recalling a 1969 meeting in Versailles

Where Flow Lenia bodies go in shape space

Twelve shape measurements place 25,167 Flow Lenia bodies in a cloud with about three effective directions. Most of its empty regions come from the measurement or from undersampling, and one band of centrally peaked bodies that still fill their footprint stays empty across 1.35 million archived bodies.

Density of archived Flow Lenia bodies in compactness and coverage, with the empty band outlined at high values of both
1,353,965 archived Flow Lenia shape vectors · 17,991 synthetic fields

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.

Native rule
Recovered rule
Orbium from the same starting cells, under the native rule and the recovered rule.

The search scored only the step-600 field, and the recovered rule keeps the body coherent through step 1,200.

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 can still reach the theorem by another route.

Two routes through an algebraic proofA schematic proof of distributivity. One branch rewrites by distributivity, the other swaps the factors and uses ring normalization. The toggle removes the direct rewrite from the illustrated search.For real a, b, c, provea(b + c) = ab + acswap factors(b + c)aringProveddistributeab + acringProved
Two routes reach a proof in this schematic.

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