Tag Archives: Tiling

A rosette in a roman mosaic is an exponential transform of a periodic tiling

In the depot of the museum of Avenches (Switzerland) lies this interesting fragment of a large roman mosaic :You see immediately that this is a rosette with rotational symmetry, except for the fruit at the center. Looking closer we see an … Continue reading

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A fractal tiling of both octahedral and icosahedral symmetry

I want to show you a fractal tiling which can be seen as a decoration of a sphere with octahedral symmetry and at the same time as another decoration of a sphere with icosahedral symmetry. It arises as the limit … Continue reading

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A variant of the Apollonian gasket with icosahedral symmetry

We modify the Apollonian gasket presented in the earlier post Apollonian gasket as a spherical fractal with tetrahedral symmetry. In an icosahedron, five triangles meet at their corners, which gives us a fivefold rotational symmetry. At the centers of the triangles … Continue reading

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Apollonian gasket as a fractal in tiled hyperbolic space

Reading the fascinating book « Indra`s Pearls », written by David Mumford, Caroline Series and David Wright, you discover that the Apollonian gasket can be created by multiple inversions at four touching circles. Three of the circles are of equal … Continue reading

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Apollonian gasket as a spherical fractal with tetrahedral symmetry

Before discussing the relation between the Apollonian gasket and tilings of the sphere, I want to present briefly the spherical kaleidoscope with tetrahedral symmetry. A tetrahedron has three different kinds of points with rotational symmetry. Four equilateral triangles make up … Continue reading

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class Point

For the dualization method we need a better data structure than for the projection method. Thus I defined a new class “Point” to represent grid-points and dual-points. It is an improved version of the class “TPoint”, see “TPoint – the … Continue reading

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Tilings and their duals

I briefly discussed the dualization method in “The dualization method” but you will need more details to be able to understand my computer code. You can find some interesting ideas in Wolfram MathWorld and in Oracle ThinkQuest. In part I … Continue reading

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