A room of living substrates.
Six GPU- and CPU-accelerated simulations that run in the browser. Each is a different thesis about what a substrate is — a lattice of spins, a field of reaction-diffusion chemistry, an asymmetric force matrix, a continuous cellular automaton, a composed envelope of physical constraints. Paint into any of them. Watch what the rules permit.
Ising
The smallest model of a phase transition.
A lattice of ±1 spins, exchange coupling J, temperature T. Metropolis or Wolff. Observables: ⟨M⟩, ⟨|M|⟩, ⟨E⟩/N, χ, Cv, the Binder cumulant. Toggle to the Tsarev social reading and the same lattice becomes a model of collective opinion dynamics.
Lenia
A creature made of field.
Continuous cellular automata. Orbium and its kin glide across a smooth substrate under a Gaussian growth rule. The Ghost Species — Orbium unicaudatus ignis var. phantasma — inhabits a σ-gradient landscape where physics itself varies in space, remembering shapes it can no longer hold.
Lenia Expanded
Four channels and a four-dimensional organism.
Prey, predator, morphogen, and the Dihypersphaerome ventilans — a 4D organism whose 2D shadow seeds the ecosystem it inhabits. Cross-coupling in the growth rules; advection along a derived flow field; the whole thing breathes through an XW/YW/ZW rotation of its fourth dimension.
Gray-Scott
Pearson's eight classes of pattern.
Two partial differential equations — substrate u, catalyst v — with feed rate F and kill rate k. Small changes in (F, k) produce mitosis, solitons, coral, worms, U-skates, spirals. A cartography of continuous parameter space with discrete classes as landmarks.
Particle Life
Emergent ecologies from an asymmetric force matrix.
Six particle types, a 6×6 matrix of attraction and repulsion — M[i][j] need not equal M[j][i]. The asymmetry is what lets predation, symbiosis, membranes, and orbital capture emerge. You can't get these from any symmetric potential.
Each substrate is a claim about what is allowed to live in it. The paper and the simulation are the same argument, read twice.