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Monthly Archives: October 2013
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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Hints for experiments
You can modify the code of the last post “selfsimilar fractals … – the code” to produce new images. A large value for the imaginary part of the constant c often destroys the mirror symmetry and gives a more dynamic … Continue reading
Posted in Fractals, programming
Tagged fractal, fractal design, Rotational symmetry, Selfsimilarity
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selfsimilar fractals from function iteration – the code
// this reproduces the image of ” selfsimilar fractals with …” // you can make your own experiments, try the codes hidden as comments // this is for the main tab of processing // it needs the code of “from … Continue reading
Posted in Fractals, programming
Tagged fractal, fractal design, processing, programming
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From pixels to coordinates – with code
This is similar to “setting up the coordinates” but goes in opposite direction. We now know the coordinates (i,j) of a pixel on the screen and we need to know the corresponding coordinates (x,y) in the complex plane. We want … Continue reading
Posted in Uncategorized
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complex numbers – the code
// see the last post “using complex numbers” for more details class Complex{ float x,y; Complex(float xp,float yp){ x=xp; y=yp; } // addition Complex add(Complex two){ return new Complex(x+two.x,y+two.y); } … Continue reading
Using complex numbers
For complex functions f(z) needed to create fractals we could calculate the real and imaginary part separately using basic arithmetic with float numbers. But this is hard to do and may cause many programming errors. It is better to use … Continue reading
Posted in programming
Tagged complex arithmetic, complex numbers, object oriented programming, programming
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selfsimilar 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 “selfsimilar images from iterated mappings of the plane“, and I got some new ideas I want to … Continue reading
Posted in Fractals, Selfsimilarity
Tagged analysis, complex function, fractal, iteration, Rotational symmetry, Selfsimilarity
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