If One Line Visits All 2,401 Hexagons, The Gosper Island Turns Rainbow | 7 Satisfying Simulations

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An empty Gosper island of dim violet hexagons waits. One line enters it and never lifts or crosses itself. It follows the Gosper curve, also called the flowsnake, through all 2,401 hexagons, each exactly once, and every hexagon takes the colour of its place along the line, red at the start and violet at the end. Seven small islands, each made of seven smaller ones, show up as patches of colour. After it come six more pictures that are built piece by piece: a Koch snowflake from 1,128 folding paper triangles, a sheet of 400 stamps, a Sierpinski triangle painted by one line in 2,187 steps, a flower of 36 petals, a wall of 120 roller strokes and a braid of 24 ribbons.

The number under each chapter title is the simulation's own count in that frame: hexagons the line has visited, triangles unfolded, stamps printed, triangles painted, petals laid, roller strokes finished and ribbons stretched.

What is exact and what is paced? The Gosper curve is the real four-level flowsnake (built from its L-system, 60-degree turns), and the arrowhead line is the real seven-level Sierpinski arrowhead curve: every small triangle it paints is one of the triangles of the gasket, and the holes stay empty. The snowflake is a geometric tiling of a three-level Koch outline, not a growing ice crystal. The stamps, the petals, the roller and the ribbons are drawings that follow a fixed timetable, not a model of printing, hands, paint or weaving. Every picture finishes on a fixed timetable, so the seed changes nothing you can count. The rules, the code and the sound are all original.