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Same rules as the 2D chaos game, just with the vertices of a polyhedron instead of a polygon: drop a point, then repeatedly move it some fraction (ratio) of the way toward a random vertex. At ratio = 0.5 a tetrahedron's four vertices produce the 3D analog of the Sierpinski triangle, the Sierpinski tetrahedron - four shrunken copies of the whole shape, one pinned to each corner, hollowing out the middle at every scale.
Unlike the 2D page, this one doesn't jump ratio to the value where neighboring copies touch corner-to-corner - working that out in 3D depends on the specific polyhedron's geometry (how its faces, not just its vertices, meet), not a single formula shared by every shape the way the regular-polygon case was. Nudge ratio by hand instead and watch the structure open up or overlap.
The five Platonic solids and the thirteen Archimedean solids come from the same data file as the Polyhedra page, which draws them as solids; the chaos game uses only their corners.
Rendered by the same point-cloud renderer as the 3D IFS and Lorenz Attractor pages, including its "color by vertex" categorical coloring - the exact 3D counterpart of the 2D chaos game's own color by vertex checkbox.
This page was created with Claude Code.