Of course we're not limited to simply two dimensions. The chaos game works precisely the same in three dimensions as well.
We simply introduce a z-axis to the game and position the anchors.
Chaos game played over 10,000,000 terations with four anchor points to form a tetrahedron
Chaos game played over 20,000,000 terations with eight anchor points to form an octohedron
Chaos game played over 10,000,000 terations for tetrahedron but not repeating any anchor points.
Chaos game played over 10,000,000 terations with twenty anchor points to form a regular dodecahedron
Below is all the regular polyhedra with the chaos game rendered for 10,000,000 iterations for different variations of the game.
| Polyhedra | Tetrahedron | Cube | Octahedron | Dodecahedron | Icosahedron |
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| Normal |
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| No Repeat |
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| No Repeat Nearest |
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