Experiment 01
Lenia
A continuous cellular automaton where mobile creatures appear without ever being programmed — just a local rule, repeated.
What is Lenia?
Lenia is a family of continuous cellular automata designed by Bert Wang-Chak Chan (a researcher then at MIT). Unlike Conway's Game of Life, where space, time, and cell states are discrete, Lenia makes all three continuous: the grid is finely sampled, time advances in small steps dt, and each cell holds a real value between 0 and 1 rather than a simple alive/dead boolean.
At each step, a convolution kernel (often ring-shaped) weighs each cell's neighbourhood; the result passes through a growth function (usually a Gaussian) that decides whether the cell should grow, shrink, or stay stable. This purely local rule, identical everywhere on the grid, is enough to give rise to organized shapes: "creatures" like the Orbium, which move, pulse, and sometimes split.
Why this is emergence
None of the creatures observed in Lenia were hand-drawn and then animated: the rule only describes a cell and its neighbours, never a global shape. Mobile isolates, oscillators, self-replicating structures — all of it results from the repeated application of a local function, not a plan. That is the very definition of emergence: a coherent macroscopic behaviour that is written nowhere in the microscopic rules.
LifeLabs does not claim these structures are "alive" in the biological sense. But they do satisfy several criteria usually associated with life: they maintain organization far from equilibrium, resist perturbation, and can disappear (extinction) or destabilize (explosion) depending on parameters. The word "creature" is a useful shorthand here, not a claim.
Pilot
Pilot the simulation
Mapping the whole parameter space
The vital signs we measure
Each run records five time series, computed at regular intervals during the simulation, which serve as "vital signs" for the observed creature:
- Mass
- the sum of all cell values — a collapsing mass signals extinction, a diverging mass signals an explosion.
- Center-of-mass speed
- the speed of the structure's center of mass — near zero for a static isolate, positive and stable for a mobile one.
- Spatial entropy
- a measure of how spatially dispersed the active cells are — it drops as the creature organizes into a compact, coherent shape.
- Compressibility
- an estimate of the structure's regularity — the more repetitive a shape, the more compressible it is.
- Active fraction
- the proportion of significantly non-zero cells — it indicates whether the creature occupies a stable portion of the grid.
