Roll 2026-1016:9
11 Rules That Turn Loose Parts Into Perfect Order
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Eleven simulations, and every one of them ends in a perfect, finished picture: 469 loose discs that seat themselves into a 12-ring rainbow crystal, squares that grow by the Fibonacci rule until the golden spiral appears, six waves that weave a rosette, a ball that lights all 268 mirror tiles of a disco ball, a scrambled picture that turns back into itself after 12 turns, a sheepdog that herds 180 sheep into a pen, 32 metronomes that settle on one beat, a zoom into the Mandelbrot set, a bouncing ball that opens 230 petals, 600 candies that ants carry to their own colour rings, and a printer that lays 4,461 beads into a rainbow vase. No talking.
This one has a single promise: every chapter ends in a picture that is as tidy as it can be. The number under each chapter title is the simulation's own count in that frame, so you can watch it climb to the finished crystal, spiral, vase or pen.
Some chapters run on real rules. The discs are pulled toward free seats that touch two others, the Mandelbrot picture is computed pixel by pixel from the real iteration, the picture in the scrambled-picture chapter is shuffled by Arnold's cat map and comes back exactly after 12 turns, and the sheepdog follows a published two-mode herding model. A few keep to a timetable so that they finish on time: the Fibonacci squares, the printer and the disco ball's bounce count follow a planned pace, the metronomes use a simple model of how their swings pull each other into step, and the ants and the sheep are steered by a small amount of planned control. The rules, the code and the sound are all original.
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