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Sierpinski Tetrahedron Cross-Sections (2D)

2D companion to the 3D Sierpinski chaos game: slice a plane through the tetrahedral point cloud and watch the cross-section change — including a hidden hexagram at half height — as you sweep height, tilt, jump ratio and the forbidden-repeat rule.

Mathematics2DModerate60 FPS⇄ 3D version

This 2D companion doesn't flatten the 3D chaos game into a triangle — that mechanic already exists elsewhere on the site as the standalone 2D vertex chaos game. Instead it does something only a genuinely 3D original makes possible: it cuts a plane through the same tetrahedral point cloud the 3D Sierpiński simulation generates, keeps only the points that land inside a thin slab around that plane, and projects them onto a flat canvas. Sweep the slice height through the middle at tilt 0° and watch a hexagram (Star-of-David) shape assemble out of clustered points — a genuine, lesser-known property of the Sierpinski tetrahedron's cross-sections, not decoration. Tilt, jump ratio, cloud density and the forbidden-repeat-vertex rule all reshape the underlying point cloud and therefore every cross-section cut through it.

⚙ Under the hood

3D chaos game in a regular tetrahedron (pₙ₊₁ = pₙ + r·(vertex − pₙ)), sliced by a plane at adjustable height and tilt; points within a thin epsilon band of the plane are projected onto an orthonormal in-plane basis and rendered on a 2D canvas.

sierpinski tetrahedronchaos gamecross-sectioniterated function systemfractal geometryplane-point intersection

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install