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 Color symmetry using the length scale of the inflated lattice
 images with 5fold symmetry and color change indicating selfsimilarity
 images of 8fold rotational symmetry and color changing mirror symmetry
 images of 10fold rotational symmetry and 2color symmetry upon rotation
 Examples of basic fivefold rotational symmetry
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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 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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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
Posted in Fractals, Kaleidoscopes
Tagged fractal, fractal design, kaleidoscope, mirror symmetry
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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
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
Posted in Selfsimilarity
Tagged Chaos and Fractals, fractal, fractal design, julia set, Mandelbrot set, Selfsimilarity
1 Comment
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