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New version of Kalles Fraktaler 2.5.9 available on http://www.chillheimer.de/kallesfraktaler/

Inflection is a word introduced to me by startdust4ever.
I take it as the terminology for how the pattern of the Mandelbrot set is affected by zooming into a point in embedded Julia set and repeated with doubled density. The pattern is doubled and wrapped around the point, and also the area nearest the point is magnified.

I am fascinated by "Julia morphing", the ability to "sculpt" the pattern by selecting the point to zoom into. However, it is always kind of a surprise to me to find out how the pattern looks like when it eventually repeats. I simply don't have a sense for it.

Stardust4ever suggested in one of his posts that we could finish a zoom sequence to a Minibrot by doubling the pattern from half of it, double again from 3/4 etc, instead of rendering it the whole way. I now know that that is hardly possible, because the nearer are of the zoom point is magnified, so it would require unreasonable high resolution.

But I experimented with a preview function - "Show Inflection", and it turned out very well. Instead of guessing how the pattern will look like when it repeats, the preview function allows us to see how it actually will turn out. I picture myself being able to create resemblance to any object in the Mandelbrot set, e.g. letters, animals, faces, Axolotl, but it is kind of hard even with this new function. But with more practice it will eventually be possible.

Here is a screenshot - the "Show Inflection" really shows how it actually turns out:
(http://www.chillheimer.de/kallesfraktaler/inflection.png)
And this only works for the standard 2nd power Mandelbrot and probably not for Burning ship either.

So you actually found this pattern when zooming 10^6 more ? Impressive feature !

I feel like you are just applying a z -> z² function to deform the image, right ? (I can't find the startdust4ever post)