Fractal tilings with three-fold rotational symmetry


A number of f-tilings with 3-fold rotational symmetry are shown below as thumbnail images. Click on the image to see a larger version. Some of these are included in "Tilings by Number of Prototile Edges", under "Hexagonal prototiles" and "Other polygonal prototiles", as well as in "Tilings by Generating Polyform", under "Prototiles based on polyhexes" and "Prototiles based on polyiamonds". For polyhex-based (shapes made from edge-matched regular hexagons) f-tilings, there are four variants for each tile, with two possible attachment points and the option of mirroring between generations. Only some of the possibilities are shown here. There are infinitely many additional polyhex prototiles, but they become less interesting as the number of hexagons in the polyhex increases, since the scaling factor becomes more extreme. Several of the f-tilings near the bottom of the page are based on polyiamonds (shapes made from edge-matched equilateral triangles), for which there are also an infinite number of possibilities.






















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