Janus Nanomotor 2D: Active Brownian Swimmer

This is the 2D counterpart to the 3D Janus Nanomotor simulator: instead of an instanced 3D sphere swarm, it solves the standard 2D active Brownian particle (ABP) equations directly — a genuinely planar model, not a flattened 3D scene. Two hundred and twenty two-tone discs (a gold catalytic cap, a grey inert half) drift across a simulated fuel bath, each self-propelled along its own heading by self-diffusiophoresis while 2D rotational Brownian motion randomizes that heading over time. Because a 2D heading has only one rotational degree of freedom (rather than the two of a free 3D orientation vector), the persistence time and long-time diffusion formulas differ from the 3D sim in a way that was checked here by direct numerical simulation, not assumed. Tune fuel concentration, particle radius and bath temperature to watch the theoretical and tracer-measured diffusion coefficients converge live, or switch the catalytic cap off to collapse the swarm back into ordinary passive Brownian motion.