Category Archives: Fractals

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 , , , , | Leave a comment

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 , , , , , | Leave a comment

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 , , , , , , | Leave a comment

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

Posted in Fractals, programming | Tagged , , , | Leave a comment

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

Posted in Fractals, programming | Tagged , , | Leave a comment

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

Posted in Fractals | Tagged , , | Leave a comment

high resolution images with off-screen drawing

In an earlier post I have shown how to make smooth images at any scale using the pdf-renderer. But you can do this only with graphics objects such as line, point, shape, ellipse and so on. It won’t work if … Continue reading

Posted in Anamorphosis, Cellular automata, Extra, Fractals, Kaleidoscopes, programming | Tagged , , , , , | Leave a comment