Fractal Related Discussion > Fractal Mathematics And New Theories

 Newton-Raphson zooming

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gerrit:
Thanks Claude, I'm going to kick around this NR zooming some more, if it works for you I must be doing something wrong.

Overshooting in KF NR is not uncommon, usually not by such extreme factors though and you can just back out to recover. Hard to bug-report as you lose the location that triggered it.

gerrit:
Got it to work, including size estimation, either with triangles, or with a rectangle. With rectangle after finding the lowest period it becomes more complicated to decide if the points surround the origin due to self-intersection if you keep original order. Isn't a triangle faster anyways (as NR zooming gets slow at great depths)?

If you continue after finding the lowest period until one of the initial points goes to "infinity" you get a few more nuclei, though it is sort of random which ones you find. See example below, I verified all the black squares in the top figure (indicating where I found them) are in fact correct by inputting the location with appropriate zoom factor determined by the size estimate into KF.

hapf:
Interesting discussions on this new forum going on...
I use triangles for this and had no issues so far except sometimes nothing is found. But
that is due to the points escaping too early, I think.

gerrit:
I managed to accelerate the Newton-Raphson part of the nucleus finding method.

Idea is to compute a reference orbit from cguess in full precision, then in the NR iterations use native precision using PT with this reference orbit. Speedup is considerable, it works on all examples I tried though I suspect it could fail if cguess is "to far" in some sense.

Perhaps something similar can be done for the box method to find the period, I haven't tried that yet.

hapf:
PT breaks down for NR and box method. It can work sometimes but is not reliable.

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