Alpha-Synuclein Aggregation (2D): Gillespie SSA + Fractal Cluster

This is a 2D-native counterpart to the 3D Lewy-body aggregation simulator: the same nucleation-dependent, autocatalytic Finke-Watzky kinetics, but solved as an exact Gillespie stochastic simulation algorithm on discrete monomer counts rather than an Euler-integrated mean-field ODE. Free monomers perform independent Brownian random walks across a 2D soma cross-section and physically stick to a growing diffusion-limited-aggregation (DLA) fibril cluster the moment a stochastic conversion event assigns them to it, producing the branched, radiating morphology believed to underlie real Lewy-body ultrastructure. A second panel plots the exact phase-plane rate law dB/dt = (1−B)(k1+k2·B) with a live marker tracing the run — a state-space view of the same lag/growth/plateau sigmoid the 3D version only shows as a time series. Tune the nucleation and autocatalytic rate constants to watch the hump reshape and the (now genuinely stochastic) lag phase shift run to run, or toggle seeding to skip it entirely.