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Category Archives: Fractals
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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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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two circles
Lately I have played around with inversion at circles trying to find some new kind of fractals. Thus I found a simple mapping that gives interesting designs. They are not fractal, instead overlapping circles appear. Inversion at a single circle … Continue reading
Posted in Extra, Fractals
Tagged concrete art, dynamics, geometric art, inversion, inversive geometry, Iterated function, iteration
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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