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Submitted on
September 28, 2012
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Cosbrot Convergence by pifactorial Cosbrot Convergence by pifactorial
Inspired by Ampersand by :iconlkmitch: (who has some fabulous mathematically inspired art), I realized that, in an escape-time fractal, the reciprocal harmonic sum of the sequence at any given point ought to be almost always convergent. The magnitude and complex argument of the convergent value can be used for simultaneous "in-colouring" and "out-colouring" of the fractal. (Points inside the fractal set will converge to zero, but you can get around this by using a small number of iterations and a logarithmic scale for the magnitude, as I have here.)

While in the case of an ordinary Mandelbrot, this colouring scheme produces colourful but not terribly exciting result, I decided to try applying it to more of my Mandelbrot variants. Cosbrot, which in the manner of Sincbrot uses the cosine function to approximate z^2 (see Sincbrot Galaxies for a somewhat confusing explanation), gave some pretty cool rainbow lightning when I tried it out.

z = 2*(1-cos(z)) + c
x = -3 ... 1
y = -2 ... 2
(x and y are swapped in the image)
:icon1080west:
1080west Featured By Owner Oct 1, 2012
:peace: :heart: :peace: :heart: Fantastic colors !! :iconcheerplz: :iconyaayplz: :iconwowplz:
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