Λ — 003Substrate

Lenia

Continuous cellular automata

Chan (2018, 2020) · Sebastian & Claude (mmxxvi)

A creature made of field — continuous space, continuous time, continuous state.

Lenia (Chan, 2018) lifts cellular automata out of the discrete grid. The neighbourhood is a smooth bell, the growth rule a smooth Gaussian, the state a real number in [0, 1]. At the right (μ, σ) the field supports stable travelling creatures — Orbium, Scutium, Ignis, a small zoo of solitonic organisms whose morphology is what their kernel permits and whose motion is what their growth rule drives. Onsager solved the Ising lattice exactly; Lenia has no closed form. We watch its solitons live and die.

Chan (2018) · Chan & Heiney (2020) · Lenia Expanded Universe

view

reading

classic species · Chan (2018)

ghost species · Sebastian & Claude (2026)

field

μ · growth centre0.150

Centre of the Gaussian growth band.

σ · growth width0.017

Tolerance band around μ. Tight → fragile.

R · kernel radius13 cells

integration

dt · timestep0.100

spf · steps/frame2×

brush · cells8

rendering

bloom strength0.45

brightness1.00×

Pre-tonemap exposure. Reinhard rolls off highlights.

playback

0 steps · 0 fps · mass 0
click to add · shift-click to erase

palette: Lantern

Orbium

The classic glider soliton — stable directed locomotion (μ=0.15, σ=0.017).

observables

total mass · Σ A(x)—

0 simulation steps
0 fps · 256² lattice · R = 13

ghost mode

In paint mode, click to raise σ (loosen physics; creatures struggle). Shift-click to lower σ (kinder physics; safe harbour).

season speed0.15

season amplitude0.25

Lenia rule (Chan, 2018)

∂A/∂t = G(K * A; μ, σ)
A(x, t) ∈ [0, 1]
G(u) = 2·exp(−(u−μ)²/2σ²) − 1

K(r) = exp(4 − 4 / (4r(1−r)))
Orbium · Scutium · Ignis
self-similar under (R, μ, σ) rescaling

what to watch

Watch Orbium for the soliton glide — it moves without deforming, its shape invariant under translation. In Lantern palette, every creature's edge shimmers a slightly different rainbow because the iridescent layer reads from the local growth field. The hot core blows out warm gold; the dissolving rim cools to violet.

Load Soup to watch natural selection on a timescale of seconds — many Orbium compete for substrate space and the colliders annihilate. Switch the view toggle to potential to see the convolution field underneath the creature; to growth to see the signed contribution that drives state forward; to composite for all three at once.