Tag Archives: iteration

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

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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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self-similar fractals with rotational symmetry from function iteration

I was looking at my posts of march 2013 on complex function iterations, see in particular “fractal surprise from complex function iteration” and “self-similar images from iterated mappings of the plane“, and I got some new ideas I want to … Continue reading

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Complex function iteration: Further results and a puzzle

I used the method of the post “Fractal surprise from complex function iteration” for the function where c is a constant. To get a better image I now use dark blue for all numbers z that grow without limit in … Continue reading

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Another surprise from complex function iteration

Playing around with my program I found a remarkable result. I used the function f(z)=z*z*z*z+z*z+0.000002 in the iteration. Because of the leading 4th power this multiplies the complex phase by four for large z. Thus the compensation is minus three … Continue reading

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Fractal surprise from complex function iteration

Recently I got the inexpensive Dover reprint of Clifford A. Pickover’s book “Computers, Patterns, Chaos and Beauty”. Part of it extends topics presented in “The Armchair Universe” by Dewdney. And there are other interesting ideas in Pickover’s book. Get it, … Continue reading

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A tiling with squares and triangles only

One can go to the other extreme and find suitable dissections of the square and the equilateral triangle without rhombs. For the square we get two different compositions of the sides. Thus we need two different kinds of triangles to … Continue reading

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