Recent Comments
Tag Archives: fractal
Fractal tiling of a sphere with octahedral two-colour symmetry
The octahedron can have a nice two-colour symmetry. We get it from putting two tetrahedrons together, making a stellated octahedron. It is an eight-pointed star and has already been discussed by Pacioli in his book “de divina proportione” in the … Continue reading
Posted in Fractals, Kaleidoscopes, Self-similarity, Tilings
Tagged color symmetry, fractal, kaleidoscope, octahedron, spherical tiling
Leave a comment
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, Self-similarity, Tiling
Leave a comment
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, Self-similarity, Tilings
Tagged Apollonian gasket, fractal, icosahedral symmetry, spherical geometry, Tiling
Leave a comment
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
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 Apollonian gasket, fractal, kaleidoscope, spherical geometry, tetrahedral symmetry, Tiling
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 event-oriented, fractal, processing, programming
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
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
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, Self-similarity, Uncategorized
Tagged fractal, Iterated function, iteration, julia set, Rotational symmetry, Self-similarity
Leave a comment
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
Posted in Fractals, programming, Self-similarity
Tagged Color, fractal, fractal design, Rotational symmetry
Leave a comment
