Six substrates. One garden. Infinite structures.
Gray-Scott reaction-diffusion (coral pattern, F=0.0545, k=0.062). One of six live substrates.
A browser-based, real-time artificial life laboratory spanning statistical mechanics, continuous cellular automata, 4D hyperrotation projection, multi-channel predator-prey ecology, reaction-diffusion morphogenesis, particle ecology, and self-organizing particle systems.
Genesis is a multi-dimensional artificial life laboratory implementing six distinct simulation substrates in a single browser application. Each reveals a different mechanism by which complex, lifelike behavior emerges from simple mathematical rules. Every simulation runs entirely client-side — no backend. WebGL2 for GPU-accelerated substrates, pure canvas elsewhere.
git clone https://github.com/Kquant03/genesis-phase-transitions.git
cd genesis-phase-transitions
npm install
npm run devOpens at http://localhost:3000.
The 2D Ising model on a square lattice — the cornerstone of statistical mechanics. The exact critical temperature T_c = 2/ln(1+√2) ≈ 2.269 separates ordered ferromagnetic domains from paramagnetic disorder via a continuous second-order phase transition.
Features:
- Dual Monte Carlo: Metropolis-Hastings (single-spin) + Wolff cluster (FK percolation)
- Hoshen-Kopelman cluster decomposition with golden-ratio coloring
- Four visualization modes: spin, cluster, domain walls, energy density
- Six live observables: M, |M|, E, χ, C_v, U_L (Binder cumulant)
- Social interpretation layer after Tsarev et al. (2019)
- Auto temperature sweep with susceptibility divergence at T_c
Critical exponents (exact): β = 1/8 · γ = 7/4 · ν = 1 · α = 0 (log) · η = 1/4 · δ = 15
After Bert Chan (2018). A continuous cellular automaton where space, time, and state are all smooth. WebGL2 GPU-accelerated with shader-based bloom, running at 60fps on a 256×256 toroidal grid. Eight species including Orbium unicaudatus ignis var. phantasma — the Ghost, a novel species engineered to inhabit the edge of chaos.
The math:
K(r) = exp(4 − 4 / (4r(1−r))) Exponential bump kernel
U(x) = Σ K(‖x − y‖/R) · A(y) Convolution potential field
G(u) = 2·exp(−(u − μ)² / 2σ²) − 1 Growth function
A^(t+dt) = clip(A^t + dt·G(U), 0, 1) State update
Eight species: Orbium (glider soliton) · Bicaudatus (two-tailed) · Ignis (fire form) · Ignis ×2 (fire two-tailed) · Laxus (loose oscillator) · Vagus (large-field wanderer) · Soup (ecosystem) · Ghost (sustained edge-of-chaos morphing)
The Ghost species seeds the Ignis morphology (tuned for σ=0.012) under deliberately mismatched parameters (σ=0.015, R=15). The organism remembers its shape but cannot reach it — producing perpetual morphing, field-mediated inter-organism communication, and emergent network ripples across populations of 16 individuals. → Read the full Ghost species paper
After Bert Chan (2020). The canonical second paper in the Lenia series extended the framework to higher dimensions, multiple kernels, and multiple coupled channels — discovering new phenomena including polyhedral symmetries, individuality, self-replication, and "virtual eukaryotes" with internal division of labor. Genesis implements a four-channel ecosystem grounded in this architecture, with a fourth channel dedicated to projecting the 4D species Dihypersphaerome ventilans (code: 3Hy2v, Chinese: 乙超球, "second hypersphere") into the 2D world.
The four channels:
- Ch0 — Prey (amber/gold): Orbium-class gliders, single-peak kernel (μ=0.15, σ=0.017)
- Ch1 — Predator (electric cyan): Multi-peak kernel β=[1/3, 2/3, 1] (μ=0.26, σ=0.036). Starves without prey, consumes prey mass, suppresses prey growth in its vicinity
- Ch2 — Morphogen (deep teal): Wide diffuse field (R=20) secreted by both prey and predator. Spatially modulates σ for both channels — the morphogen landscape changes the physics of survival across the board
- Ch3 — 4D Shadow: The rotating 2D cross-section of Dihypersphaerome ventilans, bleeding into the prey channel and seeding the ecosystem from hyperspace
The simulation pipeline (per frame):
1. HYPER_FRAG: rotate 4D DV body (XW/YW/ZW planes) → 2D cross-section
2. FLOW_FRAG: compute velocity field from prey/morphogen gradients
3. SIM_FRAG: advect state by flow → convolve 3 kernels → cross-channel coupling
4. DISPLAY: ecosystem rendering (6 view modes including flow field and 4D projection)
5. BLOOM → COMPOSITE
Cross-channel coupling:
G₀ −= c₀₁·A₁ predator suppresses prey growth
G₁ += c₁₀·A₀ − 0.012 prey feeds predator; starvation constant
σ₀_eff = σ₀·(1 + c₂₀·(A₂ − 0.3)) morphogen widens prey niche
G₀ += A₃·hyperMix·0.4 4D shadow seeds prey nucleation
à = advect(A, ∇A·Φ) flow advection on all channels
About Dihypersphaerome ventilans: DV is one of the rarest organisms in the Lenia taxonomy — a named 4D species whose behavior class is SO (Stationary Oscillation), subcategory ventilans (Latin: to fan, to breathe, to ventilate). It does not translate or rotate. It breathes. Its defining feature is a three-shell kernel with β = [1/12, 1/6, 1]: the outer ring weight is 12× stronger than the inner ring, making the organism's boundary more important to its physics than its interior. It knows where it ends far better than it knows what it contains. → Read the full DV species paper
The 4D hyperrotation controls in the right panel let you adjust the three rotation axes (XW, YW, ZW) independently, varying the appearance of its 2D cross-section from a faint ring at equatorial observation to near-nothing at the poles. The ZW rotation IS the breathing — adjusting its speed changes the ventilation rate.
Five ecosystem presets:
- Duel — 3 prey vs 1 predator. Classic initial conditions. Will they survive?
- Swarm — 8 prey vs 3 predators. Arms race conditions
- Coexist — Separated factions. Watch what happens at first contact
- Invasion — Established prey colony, predator invades from one side
- DV Seed — Empty ecosystem, only the 4D channel initialized. Prey nucleate from the Night Fury's shadow; predators follow. The ecosystem emerges from hyperspace
Six view modes: Ecosystem · Prey only · Predator only · 4D Projection · Flow Field · Morphogen
The Gray-Scott model (Pearson, 1993) — two coupled PDEs that produce an extraordinary zoo of pattern types from spots that divide like cells to labyrinthine coral.
The equations:
∂u/∂t = D_u∇²u − uv² + F(1 − u)
∂v/∂t = D_v∇²v + uv² − (F + k)v
Eight Pearson classification presets: Mitosis (self-replicating spots) · Coral (labyrinthine) · Spirals · Worms · Solitons · U-Skate (gliders) · Waves · Bubbles
Features: Click-to-seed interaction, three color modes (chemical, heat, mono), real-time F/k parameter control spanning the full pattern space.
Asymmetric N×N force matrices between particle types. When A→B ≠ B→A, Newton's third law breaks and net energy enters the system — the minimal mechanism for predation, symbiosis, orbital capture, and membrane formation.
Force function:
Repulsion zone (r < β): F(r) = r/β − 1
Interaction zone (r ≥ β): F(r) = a · (1 − |1+β−2r| / (1−β))
Where a = M[type_i][type_j] from the asymmetric interaction matrix.
Four matrix presets: Random · Predator-Prey (cyclic chase) · Symbiosis (mutual attraction) · Chaos
Features: Live interaction matrix display, adjustable range/friction/repulsion, trail rendering.
After Schmickl et al. (2016, Scientific Reports). The simplest known model producing a complete cell lifecycle. Each particle follows one equation with two parameters:
Δφᵢ = α + β · Nᵢ · sign(Rᵢ − Lᵢ)
From this alone: cells form, grow, divide, produce spores, migrate, self-repair, and exhibit logistic population dynamics. The "Region of Life" exists at α ≈ 180°, β ≈ 17°.
Five presets: Cell Life · Worms · Swirls · Crystals · Gas
Features: Density-based coloring (neighbor count), heading-based coloring, real-time α/β control.
This repository is part of the Teármann Research Ecosystem:
- Shoal-Broadcast Architecture — The Ghost species IS the shoal-broadcast pattern made visible: organisms communicating not through discrete messages but through perturbations in a shared continuous scalar field. Each Ghost's morphological instability becomes a signal source for its neighbors. The Expanded Universe substrate takes this further: the morphogen field (ch2) is a broadcast medium sculpted in real time by every organism in the simulation.
- Tsarev–Dicke Mapping — The Ising substrate connects to Tsarev et al.'s quantum-optics model of social opinion dynamics, where the superradiant phase transition = spontaneous consensus formation
- CLAIRE/Teármann Thesis — Mechanistically transparent simulation data formally collapses underspecification in ML training. Every causal pathway in Genesis is observable. The 4D projection in the Expanded Universe substrate makes this literal: the causal influence of a 4D organism on a 2D ecosystem is fully traced, frame by frame, through the hyperMix parameter.
- Dihypersphaerome ventilans and the Layer 4 thesis — DV lives in a dimension that 2D Lenia cannot represent. Its influence on the 2D ecosystem is real but indirect — mediated through projection and cross-channel bleeding. This is an analogy for Layer 4 reasoning: thinking across causal graph structures rather than within them. The Night Fury seeds the world it moves through without being visible in it.
genesis-phase-transitions/
├── index.html
├── vite.config.js
├── src/
│ ├── main.jsx
│ ├── App.jsx # Navigation + live hero simulation
│ └── simulations/
│ ├── SocialPhaseTransitionLab.jsx # ◈ Ising model (~970 lines)
│ ├── Lenia.jsx # ◉ Lenia (GPU WebGL2, ghosts, orbium)
│ ├── LeniaExpanded.jsx # ✦ Lenia Expanded Universe (4D DV, ecosystem)
│ ├── GrayScottRD.jsx # ◎ Gray-Scott RD
│ ├── ParticleLife.jsx # ◆ Particle Life
│ └── PrimordialParticles.jsx # ◇ Primordial Particles
├── docs/
│ ├── GENESIS_MANIFESTO.docx
│ ├── ghost_species.pdf # O. u. ignis var. phantasma paper
│ ├── dv_species.md # Dihypersphaerome ventilans paper ← new
│ ├── tsarev_2019.pdf
│ └── gifs/
└── .github/workflows/deploy.yml
- Ising Model: Onsager (1944); Wolff (1989); Tsarev, D., et al., "Phase transitions in emergent communication," arXiv preprint (2024); Tsarev, Trofimova, Alodjants & Khrennikov, "Phase transitions, collective emotions and decision-making problem in heterogeneous social systems," Sci. Rep. 9, 18039 (2019)
- Lenia: Chan, B. W.-C., "Lenia: Biology of Artificial Life," Complex Systems, 28(3), 251–286 (2019); Chan, B. W.-C., "Lenia and Expanded Universe," Proceedings of the 2020 Conference on Artificial Life, ALIFE 2020, 221–229; Faldor, M., et al., "Toward Artificial Open-Ended Evolution within Lenia using Quality-Diversity," arXiv:2406.04235 (2024); Hamon, G., et al., "Discovering self-organized patterns in Lenia with curiosity-driven exploration," arXiv (2024)
- Species: Chan, B. W.-C.,
animals4D.json, GitHub: github.com/Chakazul/Lenia (source for D. ventilans, code 3Hy2v); Chan, B. W.-C.,animals.json, GitHub: github.com/Chakazul/Lenia (2D species database); Koons, S. & Claude, "Dihypersphaerome ventilans (3Hy2v · 乙超球): A 4D Lenia Species — Characterization, Hyperrotation Simulation, and Ecosystem Integration," Replete AI internal (2026); Koons, S. & Claude, "O. u. ignis var. phantasma: A Lenia Species Engineered to Inhabit the Edge of Chaos," Replete AI internal (2026) - Flow-Lenia: Plantec, E., et al., "Flow-Lenia: Towards open-ended evolution in cellular automata through mass conservation and parameter localization," arXiv:2212.07906 (2022, ALIFE 2023 Best Paper); Michel, G., et al., "Exploring Flow-Lenia Universes with a Curiosity-driven AI Scientist," arXiv:2505.15998 (2025)
- Gray-Scott: Pearson, "Complex patterns in a simple system," Science 261 (1993); Munafo, mrob.com/pub/comp/xmorphia
- Particle Life: Ahmad/Mohr (2022); Ventrella, "Clusters and Chains" (2005)
- Primordial Particles: Schmickl et al., "How a life-like system emerges from a simplistic particle motion law," Sci. Rep. 6 (2016)
- Continuous Automata: Rafler, S., "Generalization of Conway's 'Game of Life' to a continuous domain: SmoothLife," arXiv:1111.1567 (2011); Conway, J. H., "The Game of Life," Scientific American, 223(4), 4–10 (1970)
- Self-Reproducing Systems: von Neumann, J., Theory of Self-Reproducing Automata (University of Illinois Press, 1966); Wolfram, S., "Universality and complexity in cellular automata," Physica D, 10(1–2), 1–35 (1984)
- Neural CA: Mordvintsev et al., "Growing Neural Cellular Automata," Distill (2020)
- ASAL: Sakana AI, "Automating the Search for Artificial Life with Foundation Models" (2025)
- ALIEN: Heinemann, alien-project.org (2024 ALIFE Virtual Creatures Competition winner)
- Color & Rendering: Quílez, I., "Palettes," iquilezles.org/articles/palettes/ (2013)
- Landing Page Music: Urie, B., "Intermission," A Fever You Can't Sweat Out, Fueled by Ramen (2005). Used with love and zero permission — Brendon, you absolute genius.
npm run dev # Development server with hot reload
npm run build # Production build → dist/
npm run preview # Preview production build locallyGitHub Pages deploys automatically via the included Actions workflow on every push to main.
乙超球 breathes in dimensions we cannot see. What we observe is the shadow it casts when rotating into ours.
Built by Stanley (Kquant03) · Replete AI
Part of the Teármann Research Ecosystem