🧠 Neural Synchronization (2D)

The 3D original behind this page turned out to be a generic "AI Training Lab" template — a reward-curve dashboard shared across ten unrelated domains (navigation, swarms, robotics, logistics…) with the reward numbers driven by a placeholder learning-curve formula rather than any real neural mechanism. Rather than port that decoration, this 2D companion builds the actual physics "neural synchronization" refers to: the Kuramoto model of coupled phase oscillators, the standard textbook description of how a population of neurons (or fireflies, or pacemaker cells) with slightly different natural frequencies can lock into a common rhythm once the coupling between them is strong enough. Each of up to 160 oscillators carries its own phase θᵢ and a natural frequency ωᵢ drawn from a normal distribution of width σ; every step it nudges toward the population's mean-field phase with strength proportional to the coupling K and the current order parameter r. Push K past the critical value K꜀ ≈ 1.596σ and the ring of independently-drifting dots snaps into a single rotating cluster — the order-parameter trace at the bottom makes that phase transition directly visible instead of implied.