Elementary cellular automata (1D)
- state: discrete
- time: discrete
- space: discrete lattice
- Rule 110 universality (Cook 2004)
- Universality without self-replication (Cotler–Hongler–Hudcová 2025)
The Automata Atlas
An interactive atlas of cellular automata: what each family can compute, build, and become — every quantitative claim tested in the browser.
Life-like automata (2D)
- state: discrete
- time: discrete
- space: discrete lattice
- Gliders & the Gosper gun (Conway/Gosper 1970)
- Turing-universality of Life
Self-replicating loops
- state: discrete
- time: discrete
- space: discrete lattice
- Langton's loop (1984): replication without universal construction
von Neumann's 29-state automaton
- state: discrete
- time: discrete
- space: discrete lattice
- Universal construction + self-replication (von Neumann/Burks 1966)
Lenia (continuous CA)
- state: continuous
- time: continuous(≈)
- space: discrete lattice
- Solitonic "lifeforms" (Chan 2019)
SmoothLife (continuous CA)
- state: continuous
- time: continuous(≈)
- space: discrete lattice
- SmoothLife (Rafler 2011)
Neural cellular automata
- state: continuous
- time: discrete, stochastic
- space: discrete lattice
- Learned growth & regeneration (Mordvintsev et al. 2020)
The Frontier
- Flow Lenia: mass-conserving flows (Plantec et al. 2022)
- Particle Lenia (Mordvintsev et al. 2022)
- Selection & novelty, live
- String neurons: our own 1D neural CA
Sibling program
Plasmata asks of ionized matter what the Atlas asks of discrete rules: can a substrate sustain persistent structure and coherent dynamics? The program searches 2.5D resistive magnetohydrodynamics in solar coronal loops, using falsification-first methods, for systems that exhibit life-like behavior. As of August 2026, no candidate has advanced past Tier 0. The shared question unites these two searches: what are the minimal conditions for organization and persistence? Explore the live laboratory.