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Sincbrot Galaxies

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Psychedelia time!
This one was inspired by driehonderdvijfenzestig by :iconbermarte:. Which may not be obvious, because the two don't really look anything alike.
The fact that bermarte's fractal is essentially a Mandelbrot set, except with the z^2 term replaced with a bell curve function, got me wondering about replacing the z^2 term with any arbitrary even function that has z^2 as the first term in its Taylor expansion. From that I came up with:
6*(1 - sinc(z)) + c
Which has the Taylor expansion:
z^2 - z^4/40 + z^6/840 - z^8/60480 + ...

The result is qualitatively very similar to a Mandelbrot set, but with a bunch of extra "foliage" on the edges and large structures to the left and right. The most interesting feature to me is that certain large regions of divergence diverge at an exceptionally slow rate. This is a rendering of one such region (the branch to the lower-right of the main Mandelbrot shape). Points in the purple region took more than 17 iterations to escape, points in white regions took more than 255 iterations.

x = 0.26171875 ... 0.45703125
y = 0.6796875 ... 0.85546875

Download to see that it's full of stars!
Image size
4552x4096px 8.46 MB
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Comments5
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BramLeegwater's avatar
Great color combination!!:D