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Lenia · Expanded Universe

Multi-channel ecosystem with a four-dimensional organism

Chan (2020) · Sebastian & Claude (mmxxvi)

A four-channel ecosystem — prey, predator, morphogen, and a four-dimensional organism leaking through.

Lenia's Expanded Universe (Chan, 2020) extends the original continuous cellular automaton with multiple interacting channels. Here three of them form an ecology — prey feed predators, predators suppress prey, and a morphogen field diffuses between them carrying a chemical memory of who has been where. The fourth channel is something else.

a four-dimensional organism

The Dihypersphaerome ventilans (Chan, animals4D) is a 4D organism whose shells match the β=[1/12, 1/6, 1] kernel topology. Rotating it through XW, YW, and ZW planes produces a 2D cross-section that “ventilates” — breathes in and out — as its fourth-dimensional structure sweeps past the plane. That shadow bleeds into the prey channel as generative seed.

Read the report →
Chan (2018) · Chan & Heiney (2020) · Chan (animals4D)
view
ecosystem preset
paint channel
Click to paint · shift-click to erase.
brush size8 cells
integration
dt · timestep0.120
spf · steps/frame
rendering
bloom strength0.55
brightness1.00×
Pre-tonemap exposure. Reinhard rolls off highlights.
playback
0 fps · 256² lattice
prey 0 · pred 0
prey 0%
pred 0%
Duel
Three prey, one predator. The simplest predation ecology — watch whether the prey find the population density to outrun the predator.
secondary views
Single-channel renderings for tuning. Flow colour-codes velocity angle; brightness is speed.
observables
prey mass · ⟨A⟩
predator mass · ⟨B⟩
Lenia Expanded rule (Chan, 2020)
∂Aᵢ/∂t = Gᵢ(Kᵢ * Aᵢ; μᵢ, σᵢ + Σⱼ cⱼᵢ Aⱼ)
− Σⱼ cⱼᵢ Aⱼ Aᵢ + h(x, t)
R=prey · G=predator · B=morphogen · A=4D
predation flash where prey ∩ predator
ventilans rate ≡ ZW rotation
channel tuning
prey · ch 0
μ0.150
σ0.017
R13 cells
predator · ch 1
μ0.260
σ0.036
R15 cells
morphogen · ch 2
μ0.150
σ0.028
R20 cells
cross-coupling · ecology strengths
predation
c01 · predator → prey0.35
How strongly predators suppress prey on contact.
c10 · prey → predator0.40
How strongly prey feed predators.
c20 · morphogen → prey σ0.20
diffusion · scent trails
c02 · prey → morphogen0.080
c12 · predator → morphogen0.040
4D rotation + flow field
Dihypersphaerome · 4D
ZW rate · breathing0.18
The ventilans rhythm. Higher = faster inhale/exhale.
XW rate0.050
YW rate0.070
W slice offset0.00
amplitude0.65
bleed into prey0.12
How much of the 4D shadow seeds prey activity.
flow field · advection
mode
strength1.20
How aggressively state advects along the velocity field.
Gradient: state flows downhill along prey gradient. Curl: perpendicular to gradient (vortices). Spiral: combination with time-dependent rotation.
what to watch for
  • Predation flashes. Where prey and predator overlap, the field turns brilliant green — the moment of contact, vivid and brief.
  • Morphogen memory.A subtle teal tint lingers after creatures move on. The field remembers who has been where, and that memory feeds the prey channel's σ — kinder physics where the trail is fresh.
  • Ventilating shadow. Load the DV Seedpreset and watch the violet wisps pulse. The rhythm is the 4D organism's rotation through its W-axis — the shadow you see is a 2D cross-section of a 4D body breathing in and out through the plane.
  • Advection currents. Switch to the Flow secondary view — colours map to velocity direction, brightness to speed. Ecosystem scale becomes fluid.