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Where There's Smoke



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=7823

Kali "Mandelbrot" (parameter plane slice at fixed dynamic coords) with the same formula as Hellbugs, except that mrabs is replaced by rabs, which sends x + yi to |x| + yi.

Parameter plane views like this are, as one might hope, helpful for finding interesting Julia sets. In particular, one can find splotches of different color which, up close, resolve into groups of "puddles" or "lakes" without internal noise/structure and close by blobs that do have structure inside. The latter tend to be squiggly curves, spirals, or other shapes that are duplicated in Julia sets taken from anywhere close by. These "lake districts" serve somewhat like minibrots, after a fashion; the Marble fractal was found this way.

This image however instead shows some structures reminiscent of quadratic M-set bulbs, but distorted into flame-like forms. If there are "lake districts" here they are found by zooming in a ways.