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Kepler's (Stellated) FractalsHop David attracted my attention to Keplerian Fractals. He replaces every horn of a stellated (non-convex) polyhedron by small self-similar polyhedron. The picture shows that we can make it in two different ways (we will obtain a II-type (solid) fractal if we combine I-type ones). |
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Interactive Kepler's Octahedron is made of
4 Tetra Flakes (hit it to get next iteration). Hop David found out that it
turns into a cube under iterations. He found "Cantor's Octahedron" beneath
the cube's surface too.
Kepler's Stellated Dodecahedron I-type, II-type (solid) Kepler's Great Stellated Dodecahedron I-type, II-type (solid). Polyhedra with many vertises are too complicated :( |
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Cantor's WebsYou will get 1D Fractal Web (may be Laces or Hedgehog :) if you start at "skeleton" of a Polyhedron. The skeleton is made of rays from the Polyhedron center to its verteses. Look at Interactive Tetrahedron Web and Pyramid Web. |
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Koch's FlakesInteractive Tetra Flake (click it) is a simple 3D generalization of the 2D Snowflake. You take a equilateral triangle, shrink it 2 times and translate 6 copies (3 of them with rotation) to get "broken" equilateral triangle. Then repeat the process.One more 3D Koch object - Interactive Cubic Flake. |