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simgrammar the grammar of simulation

mechanism

Lenia stores a continuous field A(x) in [0,1]. Each step it convolves A with a smooth ring-shaped kernel K, passes the result through a bell-shaped growth function G, and updates A by a small time step dt times G(K*A), clipped to [0,1]; certain kernel and growth parameters yield moving, self-maintaining patterns ('species'). Flow-Lenia replaces additive growth with an affinity field that moves matter along its gradient, conserving total mass, and stores the rule parameters in the matter itself, so creatures carrying different rules can coexist, collide and mix. ASAL renders a simulation, embeds the frames with a vision-language foundation model, and scores parameter sets by similarity to a text prompt, by novelty of the embedding trajectory over time, or by diversity across a population; an evolutionary optimizer then searches the substrate's parameters (Boids, Particle Life, Game of Life, Lenia, NCA).

limitations

  • Lenia creatures exist in a narrow band of parameter space; most settings die out or explode, which is what made search tools necessary.
  • Creatures are fields without discrete identity, needs or stats, so connecting them to resource economies or player goals needs extra interpretation layers.
  • ASAL scores runs with a foundation model on rendered frames, which is offline-scale compute and inherits that model's notion of what looks interesting.
  • Open-ended evolution in these substrates is a stated aim, not an established result.

appears in

the paper, 4 sections · 2 chapters · 1 episode
paper

6. Five ceilings

linked in this section of the paper

paper
paper

7. The technique landscape, 2019 to 2026

linked in this section of the paper

paper
paper

8. Where the techniques land

linked in this section of the paper

paper
paper

Appendix B. Technique catalog

linked in this section of the paper

paper
ch 8

Chapter 8. Where AI lands

named in the text

book
ch 12

Chapter 12. Keeping score

named in the text

book
ep 7

Where AI lands

on screen at 1:08 where the techniques come from

episode

relations

3 stored edges
affects

Generative content on demand

ASAL turns a text prompt into a search over simulation rules that produce the described phenomenon, a route to generating new creature rule sets from player or designer descriptions at design time.

Enables new form
affects

Natural selection

In Flow-Lenia, rules travel with matter, so selection can act on creatures that emerge from the physics itself rather than on declared fitness stats.

Enables new form
affects

Trait inheritance

Rule parameters mix where creatures meet in Flow-Lenia, giving inheritance and hybridization as a spatial process instead of an explicit genome crossover function.

Deepens

claims

3 with sources
c01high

Lenia catalogued over 400 species in 18 families of geometric, segmented, resilient lifeforms, many found by interactive evolutionary search.

More than 400 species in 18 families have been identified, many discovered via interactive evolutionary computation

Abstract

src-chan-2019-lenia

c02high

Flow-Lenia's mass conservation made localized creatures easier to find, and parameter localization let multiple species with different rules coexist and interact in one world.

Due to the mass conservative nature of Flow Lenia, most of patterns do not grow indefinitely into spatially global patterns (i.e patterns that diffuse on the entire grid also called Turing-like patterns), therefore SLPs are much more common and easier to find

Discussion

src-plantec-2023-flow-lenia

c03medium

ASAL found previously unseen Lenia and Boids lifeforms and open-ended cellular automata in the style of Game of Life, and quantified qualitative phenomena in ways that aligned with human judgment.

the discovery of previously unseen Lenia and Boids lifeforms, as well as cellular automata that are open-ended

Abstract

src-kumar-2024-asal

sources

3
Bert Wang-Chak Chan (2018-12-13). Lenia: Biology of Artificial Life. Complex Systems 28(3)
Akarsh Kumar, Chris Lu, Louis Kirsch (2024-12-23). Automating the Search for Artificial Life with Foundation Models.

provenance

runs in log/runs
2026-10-24
created2026-10-24-techniques-sim-mathtechnique
2026-10-25
reviewed2026-10-25-source-claims-pilotmaintenance