1 Line → 6,561 Cells: One Path Paints A Rainbow Square | 8 Satisfying Simulations

Bu çalışma hakkında

One line starts in the corner of an 81 × 81 grid on cream paper and snakes through it in 3 × 3 zigzags nested inside bigger 3 × 3 zigzags: Giuseppe Peano's curve from 1890. It visits all 6,561 cells exactly once, never crosses itself, and the order it passes them in colours the square from red to violet. Then seven more pictures finish: an owl in 2,048 dominoes, 36 salt ponds, a snow globe of 3,000 flakes, a 4,096-cell maze flooded with paint, a cat drawn by 88 stars, a face on 100 twisting cubes and a Flood-It board of 576 squares.

A follow-up to "1 Line → 16,384 Cells": that square was filled by a Hilbert curve in 2 × 2 steps; this one uses Peano's curve, which works in threes, so the grid is 3⁴ × 3⁴ = 81 × 81. The number under each chapter title is the simulation's own count in that frame.

What is real and what is paced? The Peano path is the exact curve from its base-3 formula. The maze is a perfect maze, and the paint fills it breadth-first, one walking step at a time. Each of the 100 cubes is a full 3 × 3 model with 54 stickers whose layers really turn; it was scrambled with 8 quarter turns and simply plays them backwards (it is not a solver). The Flood-It player is a greedy two-move lookahead, not a perfect solver. The salt-pond colours follow real salt works (green algae, then pink and red microbes, then white salt), but the drying speed is a timetable, and the stars form an invented cat, not a real constellation. Every picture finishes on a fixed timetable; the seed only changes small details. The rules, the code and the sound are all original.