Lenia

Lenia replaces the harsh on/off cells of Conway’s Game of Life with a continuous field. Each point holds a value between 0 and 1. A radial kernel measures a soft neighbourhood mass; a bell-shaped growth map decides whether that neighbourhood should increase or decrease the local value; a small time step updates the field and clips it back into range. Inside that law live remarkably stable patterns—the Lenia “animals”—that translate, rotate or shimmer while remaining themselves. They are not drawn creatures. They are solutions the update rule can carry through time.

Canonical Chan Lenia (the mass-conserving-looking but actually growth-mapped continuous CA used here) has the schematic form:

Compact form: U = K * A, \qquad A_t+dt = \bigl[A_t + dt G(U;\mu,\sigma)\bigr]_0^1

where (K) is a normalised radial kernel of radius (R), (G) is typically a Gaussian-like growth peak centred at (\mu) with width (\sigma), and ([,]_0^1) denotes clipping to ([0,1]). The world is toroidal: patterns leaving one edge re-enter opposite.

Exact official genomes

The pack embeds genomes traced to Chakazul/Lenia Python/animals.json (MIT), decoded via Lenia RLE. The default Orbium parameters match the famous creature:

• (R = 13)
• (\mu = 0.15)
• (\sigma = 0.015)

Other curated organisms (Gyrorbium, Orbium Bicaudatus, Gyrorbium Revolvens, Scutium Serratus) bring their own kernel and growth parameters. Changing (\mu), (\sigma) or (R) on the simple surface is therefore a real experiment on the growth map and neighbourhood scale—capable of sustaining, deforming or killing a creature.

Presentation is not physics

membraneStrength, activityStrength and trailPersistence are presentation-only. They help eyes track edges, motion and history. They are not Flow-Lenia mass channels, not physical membranes and not pheromone memory. Overlay modes (state, potential, growth) are scientific instruments for reading (A), (U) and (G), not alternate universes.

Not Flow-Lenia

Flow-Lenia extends Lenia with flow/mass-transport mechanisms. This sphere’s integration path is clipped Euler on a scalar field with official animal genomes. Do not describe it as Flow-Lenia.

Conway’s Game of Life established that discrete local rules can support persistent mobile patterns (“spaceships”). SmoothLife and related continuous CA asked what happens when states and neighbourhoods become continuous. Bert Wang-Chak Chan’s Lenia crystallised a clean kernel-and-growth framework and an aesthetic–scientific catalogue of organisms, documented in Complex Systems and in the open Chakazul/Lenia repository.

The animals are research objects: specific parameter genomes plus patterns that remain coherent under the update. ecospheres.ai’s contribution is faithful interactive presentation of that canonical loop with exact genomes, not a new speculative Lenia variant.

Aspect	Current implementation
Field	Scalar (A\in[0,1]) on a toroidal grid.
Kernel	Canonical Chan radial shell kernels.
Growth	(G(U;\mu,\sigma)) growth map.
Integrator	Clipped Euler step.
Genomes	Exact Chakazul/Lenia animals.json organisms (MIT), RLE-decoded.
Default Orbium	(R=13), (\mu=0.15), (\sigma=0.015), (\mathrm{d}t=0.1).
Overlays	State / potential / growth views.
Presentation-only	Membrane, activity, trail, glow, visual style, camera follow.
Public simple controls	Organism, Growth μ, Growth σ, Radius R, Overlay.
Public simple tools	Spawn, Brush, Erase.
Field actions	Reset organism, Wound, Add mass.
Showcase	Desktop Gyrorbium (preset index 0); mobile Gyrorbium Mobile (index 5).
Hero framing	Host observer camera (Reset view) plus optional engine cameraFollow (organism-centroid framing); neither changes the growth map.

The most truthful one-line description is: canonical Chan Lenia running official animal genomes with clipped Euler updates.

Self-pattern, not sprite

Track whether the bright mass rebuilds itself each step. Wound it; if it is a true Lenia animal, damage interacts with the growth law rather than sliding a decal.

Glide and gyre

Gyrorbium emphasises rotation/translation personality. Follow the centroid and any spin. Camera follow (advanced/default presentation) can help without changing physics.

Growth-map fragility

Small moves in (\mu) or (\sigma) can fatten, thin, destabilise or kill an organism. Stability is a knife-edge property of the genome, not a guaranteed “life force.”

Radius as scale

(R) changes the neighbourhood size relative to the pattern. Too small or too large a kernel relative to the creature’s structure often destroys coherence.

Potential and growth overlays

Switch Overlay to potential or growth to see why the state field is changing. Bright growth regions are where (G(U)) pushes (A) upward.

Membrane and trail illusions

Edges and wakes look physical. Remember they are drawn cues. The causal field is (A) (and derived (U), (G)).

First 30 seconds

1. Load desktop showcase Gyrorbium (or Gyrorbium Mobile on a phone).
2. Watch one full glide/gyre without touching parameters.
3. Toggle Overlay from state → potential → growth → back.
4. Trigger Wound, then wait: recovery, scar or collapse.
5. Open Orbium preset and compare calm translation with Gyrorbium’s character.
6. Nudge μ slightly off the genome value; be ready to Reset organism.

Three experiments

Experiment	Question	Do	Watch for	Why it matters
Genome identity	Is Orbium special?	Orbium → note μ/σ/R → switch organism → observe automatic genome params.	Each animal’s distinct gait and stability.	Teaches organisms as parameterised solutions.
Kill by kindness	How narrow is survival?	Stable animal → raise σ in small steps.	Fattening, oscillation, death.	Growth width is part of the creature.
Mass intervention	Can the field absorb surplus?	Add mass or Brush near the body → wait.	Incorporation, shedding or breakup.	Distinguishes self-pattern from paint.

Parameter	What it really controls	Increase it	Decrease it	What to watch
Organism	Official genome (pattern + kernel/growth defaults).	Categorical.	Categorical.	Entire creature identity.
Growth μ	Centre of the growth peak in (U).	Shifts which neighbourhood masses are rewarded.	Opposite shift.	Inflation, starvation or death of the animal.
Growth σ	Width of the growth peak.	Broader tolerance for (U).	Narrower, more fragile peak.	Stability margins.
Radius R	Kernel radius.	Larger neighbourhood scale.	Smaller neighbourhood.	Whether structure still matches the kernel.
Overlay	Which field is visualised.	Categorical instrument.	Categorical.	Reading aid only.
dt (advanced)	Euler step size.	Faster/rougher integration.	Safer, slower advance.	Numerical stability versus pacing.
Membrane / activity / trail (presentation)	Edge, motion and history cues.	Stronger drawing.	Cleaner state view.	No change to (A)’s update law.

The best first pair is Organism and μ: one selects a known solution, the other probes its growth-map identity.

Gyrorbium

Desktop showcase. A charismatic rotating/gliding official animal—best first “this is alive-looking computation” moment.

Orbium

The classic soft spaceship. Ideal for careful μ/σ/R literacy because its canonical numbers are famous and defaulted.

Orbium Bicaudatus

A related official variant; compare gait and stability with Orbium.

Gyrorbium Revolvens

Another Gyrorbium-family genome for comparative morphology.

Scutium Serratus

Different radius and growth parameters; useful to show that “Lenia animal” is a family, not one silhouette.

Gyrorbium Mobile

Mobile showcase (index 5): resolution and presentation tuned for smaller plates without changing the claim of canonical Lenia.

Recommended learning order: Gyrorbium → Orbium → Wound/Reset literacy → μ/σ experiments → other animals → Gyrorbium Mobile on small viewports.

• Spawn deposits seed/mass according to the tool’s Lenia seeding behaviour (pack: SEED).
• Brush grows/paints field mass (pack: GROW).
• Erase clears mass (pack: CLEAR).
• Reset organism restores the official pattern/genome baseline for the current animal.
• Wound removes or damages a local region to test self-repair under the growth law.
• Add mass injects material—an intervention, not food in a metabolic sense.

Lenia organisms are not biological cells, animals or microbes. They are stable patterns of a continuous CA.

Membrane, activity and trail visuals are not physical structures or Flow-Lenia channels.

This sphere is not Conway Life with blur, and it is not Flow-Lenia.

Exact animals.json genomes mean parameter fidelity to the open catalogue—not that every on-screen pixel matches one historical screenshot under all resolutions and dt choices.

Add mass is not nutrition. Wound is not pathology.

The defensible conclusion is:

A continuous local kernel and growth map can sustain mobile self-patterns whose identities are precise parameter genomes.

Lenia supplies the atlas’s purest continuous cellular automaton world with a citable menagerie. It bridges discrete Life-like imagination and smooth-field self-organisation, and it trains visitors to see creatures as solutions of an update law. Beside Neural Morphogenesis (learned rules) and Cellular Tissue (energy-minimising cells), Lenia shows a third route to persistent form: carefully tuned continuous growth.

Foundational and primary sources

1. Bert Wang-Chak Chan, “Lenia: Biology of Artificial Life,” Complex Systems 28(3), 251–286 (2019). Primary reference for the Lenia framework and organism concept.
2. Chakazul/Lenia open repository, including Python/animals.json genomes (MIT licence). Implementation provenance for Orbium and curated animals used by the engines pack.