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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
 Fractal tiling of a sphere with octahedral twocolour symmetry
 A fractal tiling of both octahedral and icosahedral symmetry
 A variant of the Apollonian gasket with icosahedral symmetry
 Apollonian gasket as a fractal in tiled hyperbolic space
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Tag Archives: fractal
Fractal tiling of a sphere with octahedral twocolour symmetry
The octahedron can have a nice twocolour symmetry. We get it from putting two tetrahedrons together, making a stellated octahedron. It is an eightpointed star and has already been discussed by Pacioli in his book “de divina proportione” in the … Continue reading
Posted in Fractals, Kaleidoscopes, Selfsimilarity, Tilings
Tagged color symmetry, fractal, kaleidoscope, octahedron, spherical tiling
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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
Posted in Fractals, Tilings
Tagged fractal, icosahedron, octahedron, Poincaré disc, Selfsimilarity, Tiling
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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
Posted in Kaleidoscopes, Selfsimilarity, Tilings
Tagged Apollonian gasket, fractal, icosahedral symmetry, spherical geometry, Tiling
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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
Posted in Fractals, Kaleidoscopes, Tilings
Tagged Apollonian gasket, fractal, hyperbolic geometry, kaleidoscope, Tiling
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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
Posted in Anamorphosis, Fractals, Kaleidoscopes, Tilings
Tagged Apollonian gasket, fractal, kaleidoscope, spherical geometry, tetrahedral symmetry, Tiling
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improved code for fractals in high resolution
I was not satisfied with the earlier code for generating highresolution fractals and I improved on it to make experimentation more rapid. Now the program first generates only a lowresolution image for the computer screen.Then the code stops the “draw()” … Continue reading
Posted in Fractals, programming
Tagged eventoriented, fractal, processing, programming
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fractals in high resolution – the code
// needs the class OutputBuffer and the improved Vector class OutputBuffer outputBuffer, activeOutputBuffer; int n,iteMax; Vector c; float rLimitSq; void setup() { size(600, 600); noLoop(); int magnification=10; outputBuffer=new OutputBuffer(magnification); outputBuffer.setUnitLength(230); outputBuffer.setOffset(0.05,0); n=6; … Continue reading