Lenia

What you're seeing

A single field of "stuff" spread over a grid — but instead of each cell being simply alive or dead, every cell holds a continuous value between 0 (empty) and 1 (full), shown here as a glow from dark through teal and amber to white. Time advances in small steps, and at every step all cells update at once by the same rule, looking at a smooth, blurry neighborhood around themselves. From this, coherent blobs assemble themselves: the default Orbium is a smooth glider that holds its shape and drifts steadily across the world, gently turning and repairing itself if you disturb it. Nothing in the rule mentions "creature" or "glider" — the structure is entirely emergent.

The rule

Lenia is Conway's Life with the integers turned into smooth curves. Where Life is discrete in state (0 or 1), discrete in space (8 neighbors), and discrete in time (one full generation per tick), Lenia makes all three continuous: states are real numbers in [0,1], the neighborhood is a wide smooth ring, and each tick advances time by a small step dt. The update has three parts:

• Convolution → potential. Each cell measures a weighted average of its neighbors, U = K ∗ A, using a smooth radial kernel K of radius R — a soft ring that is zero at the center and edge and peaks in between. This is the continuous cousin of Life "counting its eight neighbors."
• Growth mapping. The potential is run through a growth function G(u) = 2·exp(−(u−μ)² / (2σ²)) − 1, a bump that returns +1 (grow) when the neighborhood density is near a target μ, and −1 (shrink) when it is too sparse or too crowded. Width σ sets how forgiving that target is. This is Life's "born on 3, survives on 2–3" rewritten as a single smooth curve over neighbor-density.
• Clipped update. Every cell changes by a small amount, A ← clip(A + dt·G(U), 0, 1), all cells synchronously via a double buffer.

Set dt = 1, make the kernel a 3×3 box, and replace the smooth bump with a hard step that only allows the values {2, 3} — and you recover Conway's Life exactly. Lenia is what Life becomes when you take that knife-edge rule and round off all its corners. The canonical Orbium parameters shown here are μ = 0.15, σ = 0.015, dt = 0.1, kernel radius R = 13. The grid wraps at the edges (a torus), so a creature gliding off one side reappears on the other.

Why it matters

Smoothing Life's rule opens a vast continuous universe of self-organizing "creatures." Lenia is populated by gliders, rotators, and wobbling rings that move, turn, and — strikingly — self-repair after a perturbation, behaviors that the brittle discrete patterns of Life rarely manage. Like Life's menagerie of spaceships and guns, these were found by exploration: Bert Chan and others swept the parameter space by hand and by search, cataloguing hundreds of distinct lifeforms and grouping them into "species" by their kernels and dynamics. Because its world is continuous and differentiable, Lenia sits at the boundary between cellular automata and artificial life: a tractable mathematical system in which lifelike persistence, locomotion, and even rudimentary interaction arise from nothing but a local update rule.

In the wild

Be clear about what Lenia is and is not. Its creatures are mathematical artificial life, not models of any specific organism — Orbium is not a microbe and does not correspond to a real cell. Its significance is as a discovery medium and an ALife system: a place to study how self-maintaining, moving structures can emerge, persist, and adapt under a simple continuous rule, and a benchmark for open-ended evolution and self-organization research. Because the whole system is smooth and differentiable, later work has used gradient-based and learning methods to search Lenia automatically for creatures with target behaviors — turning the manual hunt that built Life's catalogue into an optimization problem. The honest claim is not "this is how biology works" but "this is a strikingly life-like phenomenon emerging from arithmetic, and a fertile sandbox for asking what life-like even means."

Try this

• With Orbium gliding, nudge μ or σ by a single notch and watch the creature mutate — it may wobble, split, bloat, or die. The mass readout tells you which: steady mass = a new stable form, mass →0 = starvation, runaway mass = the field saturating to white.
• Drag on the field to paint a smooth blob and watch it either organize into a traveling structure or dissolve back into nothing — most random shapes are not viable.
• Switch to Random soup. Random initial conditions in Lenia usually spawn evolving but short-lived lifeforms that flare and fade; finding a stable creature this way is rare, which is exactly why the catalogued animals were worth cataloguing.
• Lower dt for slower, finer time (smoother but slower motion); raise it and the integration gets coarse and the creature can shatter.

References

1. Chan, B. W.-C. (2019). "Lenia: Biology of Artificial Life." Complex Systems 28(3), 251–286. (Defines the model and the Orbium creature; exact pages per the journal listing.)
2. Chan, B. W.-C. (2020). "Lenia and Expanded Universe." Artificial Life Conference Proceedings (ALIFE 2020), 221–229. MIT Press. (Generalized multi-kernel / multi-channel Lenia.)
3. Plantec, E., Hamon, G., Etcheverry, M., Oudeyer, P.-Y., Moulin-Frier, C., Chan, B. W.-C. (2023). "Flow-Lenia: Mass conservation for the study of virtual creatures in continuous cellular automata." ALIFE 2023. (Mass-conserving variant; example of search/learning applied to Lenia.)
4. Gardner, M. (1970). "Mathematical Games: The fantastic combinations of John Conway's new solitaire game 'life'." Scientific American 223(4), 120–123. (The discrete ancestor, B3/S23.)
5. Chan, B. W.-C. "Lenia" — reference implementation and creature library, github.com/Chakazul/Lenia.