Room IV  ·  Continuous cellular automata

Lenia

Bert Wang-Chak Chan · 2019

Open in the museum

The wall text

Conway's Game of Life is brutally discrete: cells are on or off, neighbourhoods are square, time comes in ticks. Bert Chan asked what happens if you sand all of that smooth — let a cell hold any value between 0 and 1, replace the square neighbourhood with a soft ring, and replace "exactly 3 neighbours" with a bell curve.

What you are looking at is what that rule does to random noise, at the exact parameters Chan published for his first creature, Orbium. Structures condense out of the soup within a few hundred ticks and then stop changing size. Each one holds a membrane against diffusion, divides when it grows too long, jostles its neighbours, and closes the wound if you tear it open — try painting through it.

A caveat worth putting on the wall: Chan's named creatures — Orbium, Scutium, Hydrogeminium natans — are not what random soup gives you. They are solitary, free-swimming solitons, and they were found, by hand and later by search, as specific starting patterns. Soup at these same numbers reliably lands here instead, in the colony phase. Both are the same rule; they are different attractors of it.

Nothing in that rule mentions organisms, membranes, division, healing or size. There is a ring, a bell curve, and a clock.

Tear a hole with the pointer and watch it close. σ is the knife edge — a thousandth either way and the colony dissolves or runs away.

The rule, exactly

state A(x) ∈ [0,1]        kernel radius R

  K(r)  = exp( −½ · ((r − 0.5) / 0.15)² )   for 0 < r < 1
          normalised so Σ K = 1

  U(x)  = Σ K(‖y‖/R) · A(x + y)      ← "how much life is nearby"

  G(U)  = 2 · exp( −½ · ((U − μ)/σ)² ) − 1  ∈ [−1, +1]

  A(x) ← clamp( A(x) + G(U) / T , 0 , 1 )

Orbium:  R = 13   T = 10   μ = 0.15   σ = 0.015

What you can change

ControlRangeDefault
Growth centre μ0.05 … 0.40.15
Growth width σ0.003 … 0.060.015
Kernel width0.05 … 0.320.15
Time constant T2 … 3010
Kernel radius R5 … 1612
Inoculum density0.08 … 10.34
Paletteone of: Bioluminescence, Amber specimen, Deep water, Micrograph0

Renderer: WebGL2 fragment shaders. Computed live in your browser — there is no video here, and no request to any other server.

Provenance

Chan, B. W-C. (2019) Lenia: Biology of Artificial Life. Complex Systems 28(3).

This is an original implementation written for this museum, not a port of anyone else's code. If you find it misrepresents the paper, that is a bug — please say so.

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