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Tag Archives: fractal
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
fractals in high resolution
Fractal images are a good reason to draw offscreen in highresolution, as discussed in an earlier post. Looking at the lowresolution image of “selfsimilar fractals …” we need some imagination to see that it is really selfsimilar. Too much details … Continue reading
Coloring the Julia set
The Julia set of a function f(z) in the complex plane has all points z that remain finite upon iterations of the function. In the last posts I have used expanding functions to get fractal images from iteration, as discussed … Continue reading
Posted in Fractals, Selfsimilarity, Uncategorized
Tagged fractal, Iterated function, iteration, julia set, Rotational symmetry, Selfsimilarity
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Rainbow colors
We can define a continuous number x of iterations needed to reach the critical radius R. Note that if the nth iteration of f(z) equals R then x=n, and if the (n1)th iteration equals R then x=n1. For values inbetween … Continue reading
Posted in Fractals, programming, Selfsimilarity
Tagged Color, fractal, fractal design, Rotational symmetry
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