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

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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 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

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Hints for experiments

You can modify the code of the last post “self-similar 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

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self-similar fractals from function iteration – the code

// this reproduces the image of ” self-similar 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

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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

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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

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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

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