Each tile on the sheet is a small patch of cortex holding two coupled population firing rates: excitatory E and inhibitory I (both 0–1, the fraction of cells active right now). Every patch updates by the Wilson-Cowan rate equations — the founding model of population-level (non-spiking) computational neuroscience:
τ_E dE/dt = −E + S(a_EE·E − a_EI·I + P + D·∇²E − θ_E)
τ_I dI/dt = −I + S(a_IE·E − a_II·I − θ_I)
S(x) = 1 / (1 + e^(−x)) [sigmoid activation]
- External drive P — background input to the excitatory population. Below a threshold the sheet stays quiescent; cross it and every patch locks into a sustained excite/inhibit limit cycle.
- Inhibitory coupling aEI — how hard the inhibitory population suppresses E. Turn it down and excitation runs away toward synchronized sheet-wide bursting, similar to the E/I imbalance implicated in seizure dynamics; turn it up and activity is damped out.
- Spatial coupling D — the diffusion term ∇²E that lets a patch's excitation leak into its four neighbors. At D≈0 each patch oscillates on its own phase (incoherent flicker); raising D lets a locally triggered burst propagate outward as a traveling wave and entrain the sheet into synchrony — the same mechanism proposed for traveling alpha/gamma waves across visual cortex.
- Inject stimulus pulse — kicks E to 1 in a small patch, letting you watch a single burst spread (or fail to spread) under the current parameters.
Real-world relevance: Wilson & Cowan (1972) introduced this two-population rate model to explain cortical rhythms without simulating individual spikes; it remains a standard tool for modeling EEG-scale oscillations, traveling cortical waves, and how a shift in excitation/inhibition balance can tip healthy rhythmic activity into pathological synchronized bursting.