The 3D version renders 484 independent cortical columns that each compete for ocular territory in isolation. This 2D companion models the same underlying Hebbian competition but adds the piece the 3D per-column model leaves out: real ocular-dominance columns don't form independently — neighboring cortex talks to itself. A Mexican-hat lateral interaction (short-range excitation, longer-range inhibition, after Swindale 1980 and Miller, Keller & Stryker 1989) couples every column on a continuous 2D field, and that coupling alone — starting from nothing but random noise — spontaneously organizes the field into the periodic stripes real visual cortex actually shows:
S = wL − wR (per-column ocular-dominance index)
near(S) = box-average of S, radius r1=1 (local excitatory pool)
far(S) = box-average of S, radius r2=5 (broader inhibitory pool)
lateral = β·(near(S) − far(S)) (Mexican-hat term, β=1.5)
dwL/dt = η(age)·(aL·r − k·wL) + κ·lateral κ=1.0, fixed — NOT PNN-gated
dwR/dt = η(age)·(aR·r − k·wR) − κ·lateral
then renormalize wL+wR = 1 (same fixed synaptic resource)
The direct Hebbian eye-competition term is gated by the identical critical-period brake as the 3D model, η(age) = ηmax/(1+6·PNN²) with PNN=age/100 (or 0 under ChABC) — perineuronal nets constrain the thalamocortical synapses that carry eye-specific signals. The lateral field-organizing term runs at its own fixed rate κ, deliberately not PNN-gated: the intracortical horizontal connections that generate the stripe geometry are wired early in cortical microcircuit development, while it is specifically the eye-competition synapses that critical-period plasticity opens and closes.
Standalone verification (Node, no dependencies): wL+wR stayed conserved to floating-point precision (<3×10⁻¹⁶) over 400 steps; deprive-left produced a negative mean ODI and deprive-right a positive one every run; at fixed simulated time, |ODI shift| under left-deprivation was ≈0.28 at age 0 vs ≈0.08 at age 100 (PNN brake) — restored back to ≈0.28 under ChABC — confirming the critical period behaves identically to the 3D model even with lateral coupling active; and doubling the inhibition radius r2 (5→10) roughly doubled the measured stripe wavelength (9→15 grid columns via autocorrelation), confirming the pattern is a genuine, tunable Turing-type instability and not a rendering artifact.
- Deprive L / R — collapses that eye's drive to 20% of normal, same as the 3D model; the field's mean color shifts toward the open eye but the local stripe geometry persists underneath.
- Age — scrubs the critical-period clock; higher age thickens the simulated PNN brake and slows (but does not stop) the eye-competition term specifically.
- ChABC — digests the PNNs at any age, forcing the brake to zero and reopening full eye-competition plasticity, exactly like the enzymatic experiments it's named for.