Model classes

A class describes the mechanics a specification must expose. It does not grant biological meaning or scientific validity.

connectome-derived

Canonical equation:

v_i(t+1) = (1 − 1/tau_m)v_i(t) + Σ_j W_ij s_j(t) + I_i(t)
s_i(t+1) = [v_i(t+1) > theta_i]

Sourced data: Published neuron identities, adjacency, synapse counts, and anatomical annotations.
Design choice: Neuron dynamics, weights derived from counts, thresholds, delays, input mapping, and readout.
Typical S and c scale: S grows with neurons plus edges; c ranges from moderate for sparse integer stepping to high for dense/conductance-based updates.
Datasets/refs: FlyWire adult Drosophila brain connectome (doi:10.1038/s41586-024-07558-y); Cook et al. C. elegans connectomes (doi:10.1038/s41586-019-1352-7).
Rejected at the gate: "simulates a brain", "the fly sees", "reconstructs consciousness".

∂u/∂t = D_u∇²u − uv² + F(1 − u)
∂v/∂t = D_v∇²v + uv² − (F + k)v

Sourced data: A published equation, measured coefficients where available, empirical initial/boundary data.
Design choice: Grid resolution, timestep, stencil, boundary conditions, non-data parameters, visual mapping.
Typical S and c scale: S is species × grid cells; c scales with grid area, species count, stencil width, arithmetic.
Datasets/refs: Pearson, Complex patterns in a simple system (doi:10.1126/science.261.5118.189); Turing, The chemical basis of morphogenesis (doi:10.1098/rstb.1952.0012).
Rejected: "models real morphogenesis", "recreates an embryo", "proves a biological mechanism".

dθ_i/dt = ω_i + (K/N) Σ_j A_ij sin(θ_j − θ_i)

Sourced data: A published coupling graph, measured intrinsic frequencies, recorded phase observations when present.
Design choice: Coupling strength, integrator, timestep, initial phases, boundary behavior, order-parameter readout.
Typical S and c scale: S is one/several values per oscillator; c is low for local sparse coupling, higher for dense all-to-all.
Datasets/refs: Kuramoto (doi:10.1007/BFb0013365); Strogatz, From Kuramoto to Crawford (doi:10.1016/S0167-2789(00)00094-4).
Rejected: "models the grid", "models the brain", "demonstrates neural synchrony in vivo".

a_(t+1)(x) = R({ a_t(x + delta) : delta ∈ N })

Sourced data: A published transition rule, neighbourhood, initial condition, or measured lattice when actually used.
Design choice: Lattice dimensions, boundary conditions, update schedule, encoding, perturbations, rendered interpretation.
Typical S and c scale: S is cell count × per-cell state; c low for compact local integer rules, higher with continuous kernels.
Datasets/refs: Chan, Lenia (doi:10.25088/ComplexSystems.28.3.251); Wolfram, Statistical mechanics of cellular automata (doi:10.1103/RevModPhys.55.601).
Rejected: "is alive", "evolves biologically", "models a real organism".

θ_i(t+1) = arg(Σ_{j: |x_j − x_i| < R} exp(iθ_j(t))) + η_i(t)
x_i(t+1) = x_i(t) + v · [cos θ_i, sin θ_i]

Sourced data: Measured trajectories, population counts, interaction ranges, or a published behavioural rule where available.
Design choice: Agent policy, collision handling, noise process, environment, initial placement, aggregate metrics.
Typical S and c scale: S grows with agents and per-agent variables; c ranges from moderate (spatial indexing) to high (all-pairs).
Datasets/refs: Vicsek et al. (doi:10.1103/PhysRevLett.75.1226); Reynolds, Flocks, herds and schools (doi:10.1145/37401.37406).
Rejected: "predicts animal behaviour", "models a real population", "demonstrates collective intelligence".

Other classes are accepted when S, f, sigma, and tau are concrete and the provenance gate passes.