Active Matter: MIPS (2D): Self-Propelled Particles & Crowding-Induced Clustering

A 2D canvas companion to the 3D active-matter simulation: hundreds of self-propelled disks (active Brownian particles) drift along their own slowly-rotating heading at a constant self-propulsion speed, colliding only through short-range repulsion — there is no alignment rule and no attractive force anywhere in the model. Each particle's effective forward speed is reduced by how crowded its immediate neighbourhood is, so a particle that gets jammed near others slows down, which keeps it there longer, which crowds the area further. Tune packing fraction φ and self-propulsion speed v₀ high enough and this purely kinetic feedback loop — motility-induced phase separation, MIPS — spontaneously splits a uniform gas of particles into dense, slow-moving clusters surrounded by a fast, dilute gas, tracked live by a largest-cluster order parameter.