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Systems
System · Continuous cellular automaton

Maths grows creatures.

Conway's Game of Life uses a binary grid and a 3×3 neighbourhood. Lenia keeps the same idea but makes state continuous and the neighbourhood a smooth radial kernel. The result is uncanny: small concentrations of substrate organise themselves into things that swim, rotate, divide. Bert Chan published the formalism in 2019. The field is still expanding.

Presets
Custom — drag μ and σ freely
Equations

One update rule, infinite zoology.

Each cell holds a value between 0 and 1. Each step, every cell looks at its neighbours via a smooth radial kernel K, asks the growth function G whether the sum is right for life, and adjusts itself by a small dt. Run that on a grid and creatures appear.

At+dt = clip( At + dt · G(K ∗ At) , 0, 1 )
G(u) = 2 · exp(− (u − μ)² / 2σ²) − 1
A · Substrate, continuous in [0, 1]
K · Kernel — radial Gaussian shell, R = 13 px
∗ · Convolution: weighted average over neighbourhood
G · Growth function — Gaussian-shaped, output [-1, +1]
μ · Growth centre — concentration where life thrives
σ · Growth width — tolerance around μ
Story

From rule-set to creature.

  1. 1970 — Conway draws Life.

    John Conway publishes the Game of Life in Scientific American. Three rules on a binary grid produce gliders, oscillators, and the surprising result that simple rules can encode universal computation.

  2. 2019 — Chan makes it continuous.

    Bert Chan replaces the binary grid with continuous values and the 3×3 neighbourhood with a smooth radial kernel. The discrete glider becomes Orbium — an actual swimming creature with soft edges that holds its shape over millions of timesteps.

  3. 2020-2023 — The zoo grows.

    Researchers catalogue dozens of new species: Geminium that divides, Tricicum that cooperates, Aquarium ecosystems where creatures eat each other. The Lenia repository becomes a living taxonomy of artificial life forms.

  4. 2023+ — Flow Lenia and mass conservation.

    Plantec et al. extend Lenia with mass conservation — substrate cannot appear or disappear from nothing, only flow between cells. Creatures now have to genuinely metabolise: take material in, give material back. Closer than ever to actual biology.

Sources