Smooth 1D Colors #5

fractal 16

Obviously, this image is not meant to be visually appealing. It is an example of what goes wrong. Fractal artists see these things quite often, and they are quickly remove from the hard drive and computer memory. Thus propagating the illusion that all fractals are pretty.

So what went wrong, and why? This image is deep zoom into an interesting area of the Mandelbrot set called a Misiurewicz point. The problem is the palette is set to the same scale as in the previous image. You can see the same color steps if you look at the few areas that are not just random colors.

If you have a map, this Misiurewicz point is near -0.2073 + 0.6947i. The horizontal (x) range of the image is +/- .0004.

What is most significant is that the escape count ranges from 75 to 1921, with average value of 500 (and for the statistic nerd, standard deviation of 22.17). These are much larger numbers, distributed over a larger range than in the previous image. So most pixels get assigned a (fapp) random color with no apparent correlation to adjacent pixels.

In the previous image the escape count range was 2 to 481, with average 4, and sd=2.18. Many fewer colors, and smaller variations.

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