• December 11, 2017, 03:51:46 PM

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Author Topic: (Kalles Fraktaler) M-set zoom  (Read 766 times)

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Offline gerrit

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(Kalles Fraktaler) Re: M-set zoom
« Reply #45 on: November 26, 2017, 02:20:54 AM »

Offline gerrit

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Re: M-set zoom
« Reply #46 on: November 29, 2017, 12:24:45 AM »
Four different iterative zooms into the same embedded Julia set.
http://persianney.com/fractal/v/k84.html

Offline 3dickulus

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Re: M-set zoom
« Reply #47 on: November 29, 2017, 05:22:03 AM »
 O0
Resistance is fertile... you will be illuminated!

https://en.wikibooks.org/wiki/Fractals/fragmentarium

Offline Fraktalist

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Re: M-set zoom
« Reply #48 on: November 29, 2017, 11:50:18 AM »
beautiful images gerrit!

this whole thread is pretty much exactly what we had in mind when we came up with the idea of "personal" image-threads . Somehow the idea hasn't caught on yet with our users, maybe it's too hidden. Would you mind if I move this thread there?

Offline gerrit

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Re: M-set zoom
« Reply #49 on: December 01, 2017, 01:59:25 AM »
http://persianney.com/fractal/v/k89.html

A technical exercise in tree building using a manual version of the method explained here: https://mathr.co.uk/blog/2017-11-09_efficent_automated_julia_morphing.html.

Recipe is to zoom in (Z) on a Misiurewicz point (in this case a terminal point), then go into a hyperbolic component until you get a bifurcation or doubling (B). Each doubling generates another tree node. For this exercise I tried to make the branches equal length by longer Z-zooms near the beginning (those branches end up at the rim). Didn't get it exactly right but not too bad. For this one the sequence was:
Z(30)-B-Z(20)-B-Z(10)-B-Z(10)-B-Z(10)-B-Z(10)-B(+)
where the numbers indicate the length of the zoom as measured by how many double spirals I pass and the last B(+) is a period quadrupling.

A nice feature of KF is that the B zooms (which almost square the zoom depths) which are tedious to do manually can be done automatically with the NR method. For this location it is right on, but for other locations it may over or undershoot and you have to search a bit after each doubling.

These NR zooms are a bit like going through a portal or a wormhole which I tried to capture in the animation.

Offline gerrit

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Re: M-set zoom
« Reply #50 on: December 06, 2017, 04:41:50 AM »


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