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 Quasiperiodic design with 8fold rotational symmetry from 4dimensional space
 Rotational symmetry from space with an even number of dimensions
 Periodic design with 3fold rotational symmetry from 3dimensional space
 Inversion symmetry doubles the rotation symmetry for an odd number of dimensions
 quasiperiodic patterns of 5fold symmetry from 5 dimensional space
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Category Archives: Fractals
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
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
high resolution images with offscreen drawing
In an earlier post I have shown how to make smooth images at any scale using the pdfrenderer. 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 Geometry, image resolution, pixel, processing, programming, smoothing images
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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
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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