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

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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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improved code for fractals in high resolution

I was not satisfied with the earlier code for generating high-resolution fractals and I improved on it to make experimentation more rapid. Now the program first generates only a low-resolution image for the computer screen.Then the code stops the “draw()” … Continue reading

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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

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fractals in high resolution

Fractal images are a good reason to draw off-screen in high-resolution, as discussed in an earlier post. Looking at the low-resolution image of “self-similar fractals …” we need some imagination to see that it is really self-similar. Too much details … Continue reading

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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

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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 n-th iteration of f(z) equals R then x=n, and if the (n-1)th iteration equals R then x=n-1. For values in-between … Continue reading

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