Lenia
Continuous cellular automata — Conway’s Game of Life generalized to continuous space, continuous states, and continuous time. Watch creatures glide, pulse, and self-organize from smooth mathematics.
About this lab
From discrete to continuous
Conway’s Game of Life operates on a grid of cells that are either alive or dead, updating in discrete steps by counting live neighbors. Lenia, introduced by Bert Wang-Chak Chan in 2018, generalizes every aspect of this framework to the continuous domain. Cell states become real numbers between 0 and 1. The neighborhood becomes a smooth ring-shaped kernel. The birth/death rule becomes a continuous growth function. Time advances in small increments rather than discrete jumps.
The growth function
At each point in space, Lenia convolves the state field with a ring-shaped kernel
K(r) to compute a local potential U. This potential is then
passed through a growth function G(U), typically a Gaussian bell curve
centered at μ with width σ:
G(u) = 2 · exp(-(u - μ)² / (2σ²)) - 1
When the local potential matches the growth center μ, the cell grows. When it deviates too far, the cell shrinks. This simple mechanism — grow when the neighborhood density is “just right” — gives rise to astonishingly complex creatures that move, rotate, split, and interact.
Creatures and taxonomy
Chan discovered hundreds of distinct lifeforms in the Lenia universe, each associated with specific parameter ranges. Orbium is a smooth glider that moves steadily across the field. Geminium is a self-replicating creature that splits into two copies of itself. Scutium is a stationary oscillator, pulsing in place. These organisms are not programmed — they are emergent solutions to the continuous update rule, stable attractors in an infinite-dimensional dynamical system.
Why it matters
Lenia bridges cellular automata, partial differential equations, and artificial life. Its creatures exhibit behaviors — locomotion, homeostasis, self-repair — that are hallmarks of biological life, yet arise from purely mathematical rules with no explicit programming. It raises deep questions about what “life” means and whether complexity requires discrete structure or can emerge from smooth, continuous dynamics.