Tag Archives: fractal design

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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A fractal kaleidoscope

– whatever that means. I got the idea from the exterior snowflake and the Koch snowflake. They both are fractal curves and are discussed in Wikipedia and Wolfram math world. But I slightly modified the iteration scheme. I start with … 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: The movie

The movie shows the images as discussed int the earlier post “Fractal surprise from complex function iteration” for a decreasing value of the constant c. The program of the last post creates the movie frames. The movie begins with c=0.4 … Continue reading

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Fractal surprise from complex function iteration: The code

//  here is the program for the last post //  Fractal surprise from complex function iteration //   simply use it in processing 1.5 (I don’t know if it works in the new version 2.) // you can download it from … Continue reading

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