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Author Topic: Postcards from the M-set  (Read 2743 times)
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jwm-art
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« on: February 06, 2017, 12:03:17 AM »

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jwm-art
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« Reply #1 on: February 06, 2017, 12:08:52 AM »


(2560x1440)
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Dinkydau
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« Reply #2 on: February 06, 2017, 01:12:49 AM »

Nice
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jwm-art
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« Reply #3 on: February 06, 2017, 01:47:18 AM »

I want to push deeper down, but my program (MDZ) is too slow. Nothing fast & deep on Linux I'm aware of :-(
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claude
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« Reply #4 on: February 06, 2017, 04:31:36 AM »

Kalles Fraktaler works in WINE (either x86 or x86_64 afaik, I use the 32bit one on my amd64 Debian).

I should really clean up my own program so it's usable by other people, if you're adventurous you could take a look: https://code.mathr.co.uk/mandelbrot-perturbator
And there is my older experiment with OpenGL (though it turns out the CPU-based perturbator is faster): https://mightymandel.mathr.co.uk/
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #5 on: February 06, 2017, 12:05:49 PM »

The 2nd image is very dense nice
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No sweat, guardian of wisdom!
jwm-art
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« Reply #6 on: February 06, 2017, 12:14:15 PM »

Thanks.

Yes I found Kalles Fraktaler works in WINE last night. I don't have a Windows install on the same machine to compare speeds though.

I took a quick peek at the source for it too, way beyond my level of maths which is very basic (I'd struggle to scrape a high school grade with it ) - I enjoy the images on mathr.co.uk!
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jwm-art
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« Reply #7 on: February 13, 2017, 08:36:08 PM »

Two alternative colour maps of the same point:
"Self Portrait (alt1)"


"Self Portrait (alt2)"


Third in a series (of which only this one is rendered large). Was intended to go far deeper but MDZ crashed during calculation of one of the small renders along the way.
"pcman3"

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UnderGeorge
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« Reply #8 on: February 16, 2017, 07:48:36 AM »

Beutiful!! Good job jwm. Im not there yet where i can create something like this but ill get there smiley
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simon.snake
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simon.fez SimonSideBurns
« Reply #9 on: February 16, 2017, 06:19:44 PM »

Beutiful!! Good job jwm. Im not there yet where i can create something like this but ill get there smiley

Yes, me neither.  I will one day crack the way to find these beautiful structures, but I'm not quite there yet.  I do find some interesting (to me) stuff, but it's a rather slow learning curve.

One way (seeing that many members post coordinates with their pictures) would be to find out which way they went by creating a zoom movie and studying the routes taken.
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To anyone viewing my posts and finding missing/broken links to a website called www.needanother.co.uk, I still own the domain but recently cancelled my server (saving £30/month) so even though the domain address exists, it points nowhere.  I hope to one day sort something out but for now - sorry!
jwm-art
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« Reply #10 on: February 17, 2017, 02:11:17 AM »

Thanks for the compliments.

I don't get the maths of it, but here's some general rules that apply as I understand it:

* The closer you zoom near the interior - the more the detail density increases (ie more iterations are required to fill in the details & slower to render)
* The further you zoom along a spike toward the interior - the more densly packed the spirals become
* The further you zoom away from the interior - the detail decreases (ie less iterations required & faster to render)
* Zooming following a feature increases the repetitions of that feature
* The first step to finding a minibrot is to identify two of the same form opposite each other.

Look at it as a continuum.

Of straight arms to spiral arms, low density to high density, 1 arm to infinite arms.

Mix & Match.

Some features will make some lessons easier than others. When zooming and you discover something in one area, try and then apply that to almost the opposite area where you wouldn't expect it to happen.

Back to the continuum, there it is again between the main mandelbrot, through minibrots, down to embedded julia sets. Think about how you find an embedded julia set and then apply that to where you wouldn't expect it. Ie, you don't need to zoom directly into a minibrot to create an EJS, they're sitting right there in the main one all along!

What is it that creates an Embedded Julia Set? Zoom distance is all. And perhaps following a defined pattern - a minor detail (understatement).

Define patterns of zooming, count everything, repeat.

Mix & Match.
« Last Edit: February 17, 2017, 02:31:04 AM by jwm-art » Logged
Dinkydau
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« Reply #11 on: February 17, 2017, 07:41:17 AM »

The way I look at it, an embedded julia set is a doubling of a minibrot. If you zoom past a minibrot there will be embedded julia sets. Julia sets can be thought of as the result of infinitely many morphings. I think that has something to do with the increasing symmetry to infinity around minibrots.
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jwm-art
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« Reply #12 on: February 17, 2017, 05:08:34 PM »

pic1:


pic2:




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jwm-art
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« Reply #13 on: February 17, 2017, 05:30:58 PM »

A continuation of the above two, taking same steps for both.
In both cases they just step beyond long double precision into arbitrary precision:

pic3:


pic4:




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jwm-art
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« Reply #14 on: February 21, 2017, 08:36:42 PM »


(2560x1440)
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