whatA few hundred elastic disks in a box, every one launched at EXACTLY the same speed in a random direction. Equal masses, perfect collisions -- each merely swaps the pair's velocity components along the line of centers, conserving energy to the last bit (the HUD posts the drift).

whyThe claim: collisions alone forge the curve. Nothing tells a disk to be fast or slow; nothing draws from any distribution. Yet the speed histogram -- a needle-thin spike at launch -- melts, spreads, and settles onto the Maxwell-Boltzmann curve (in two dimensions, the Rayleigh form), drawn from the gas's own measured energy, never fitted. The distance between histogram and curve is measured live, and it only falls. Click to inject one particle at five times the typical speed: it sheds its excess in a dozen collisions and disappears into the crowd.

howFixed-step dynamics with a spatial hash; equal-mass elastic impulses are exact, so the energy ledger sits at rounding error. The guide curve uses sigma^2 = <v^2>/2 from the live gas. One integer seeds every launch angle and the injections.