Used to see these as demos oh how fast a processor wasFor me, fractals are the essence of the universe.
I like Benoît Mandelbrot.
I'm waiting for others who want to talk about fractals. For now, anything about them.
For things like Mandelbrot, the colors are assigned by the number of iterations it takes for iterated calculations to "escape" - i.e.: how long it takes for, given \(z_{i+1} = f(z_i)\) (initialized to some initial complex number in the plane), \(\left|z_i\right|^2 > r^2\) for some "radius" \(r\). If, after a certain number of maximum iterations it does not "escape," that point (the pixel corresponding to the starting point) is colored black. The more iterations you let a fractal run through, the sharper your edges will be. The points that do not "escape" and are colored black are considered part of the Mandelbrot set. The Julia sets are a subtype of the Mandelbrot set (indeed; you can form the Mandelbrot set from all the Julia sets).Used to see these as demos oh how fast a processor was
how do you convert a number to those lovely plots
is it just real and imaginary,
how do they assign colours ?
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