12 Most Satisfying Physics Simulations (A Three-Body Orbit Draws A Figure-Eight) 🌈

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21 planets start on scattered orbits of their own, and one by one they ease onto a single figure-eight until all 21 travel it together. Three of them, the ones with white rings, are the real figure-eight solution of the three-body problem, integrated from its known starting values; the other 18 are placed on the same curve, spaced evenly around it. Eleven more pictures follow, each grown from one rule: a point that jumps 200,000 times into a silk sheet, 64 Lissajous curves in one table, 40,000 numbers walked in a spiral until the primes line up, 21 square cuts that leave a golden spiral, 30 days of Moon phases, 300 mud cracks, one pencil stroke over 513 lines, a pyramid of 385 cannonballs, a million escaping paths of z² + c, a ring of 64 magnets and a city of 5,000 windows.

The number under each chapter title is the simulation's own count in that frame: planets on the figure-eight, points plotted, curves closed, numbers walked, squares cut, days, cracks, lines drawn, balls placed, escaping paths, magnets in the chain and windows lit.

What is exact and what is paced? The figure-eight is computed: three equal masses started from Simó's initial values and integrated with RK4 over one period (it closes to within 2e-8). Only those three obey gravity; the other 18 planets are passengers drawn on the same curve, and when each one joins is set by a timetable. The silk sheet is the Clifford map (a = -1.4, b = 1.6, c = 1.0, d = 0.7) iterated for real, the glowing figure is a true Buddhabrot (orbits of z² + c that escape within 400 steps), every cell of the table is the real curve (cos aθ, sin bθ), and the spiral really holds 4,203 primes up to 40,000. The 17,711 x 10,946 sheet is cut by Euclid's algorithm, so every square side is a Fibonacci number. 1² + 2² + ... + 10² = 385 balls, packed the way real shot is stacked. The pencil follows a true Euler circuit, so each of the 513 lines is drawn exactly once. The magnets' pull is an eased path, not a solved force; the Moon's phase comes from its angle on the orbit, with the 29.5-day month drawn as 30 equal squares; the cracks follow a simple rule (each stops where it meets another), not a stress model; and the city's windows follow a timetable. The rules, the code and the sound are all original.