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Author Topic: Parallel evolution  (Read 683 times)
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Dinkydau
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« on: May 07, 2014, 02:40:16 AM »



Mandel Machine, Mandelbrot set

I have been able to extend the zoom method used for "Evolution of trees" to be able to do MUCH more! I hope to be back into the game for a while. Also I can't wait for the promised Mandel machine update which would give it arbitrary zoom depth and Pauldelbrot's glitch detection algorithm.

Parallel evolution refers to what is going on in the zoom method. Basically, evolution of trees had an "error" which caused all the shapes to appear in pairs of two (which originally I didn't want), but I found that the cause of it is that there are simply two rows of shapes which can be manipulated separately! I didn't realize that before. That means we can now have, so to say, parallel evolution lines in one shape.

Even better: this can be extended to more than just two. The only difficulty present is that those shapes lie at ridiculous depths. Since perturbation, the patience required to perform the actual zooming exceeds the patience required to sit trough the render time.

Code:
Re = -1.76893852196162866232913272174651812211375855953142166494934806348393251001753312790521558162720496673840961742929525898392480097516741602296745678571239776899772713991149241989390636889897652947212611234485549867941881225882869272742226582689916763913250056105782813225823973694454058560192322197669382409732677168940204809256
Im = 0.00283024452997144177363798354216474791454299287519103133102120111940094688883587061798090121922341180630474583284444593505689515886069478467899126927820796840459774407836450849332591774744267120960112789423535452999756119644655234943441627388310057141849803508891422998221927001498440210429589603645602871007287670148492126643

Magnification:
2^1075
4.0480450661462123670499069343783 E323
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Kalles Fraktaler
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« Reply #1 on: May 07, 2014, 12:58:28 PM »

Lovely!
We should do more Julia morphings!

Yeah, it takes some time to reach these depths.
What I usually do in Kalles Fraktaler, and it connects with your question in the KF thread, is that I usually select a large zoom level, 32 for 640x360 resolution. I then use the left mouse button (I don't even have a mouse with a scroll wheel) and this is a fast way to reach at least e200 within some minutes. You can do the math on how many times I need to click with the mouse smiley Exploring beyond e300 is a slower process, especially for Julia morphing when much of the sequence is centering.
When I found the 'perfect' shape I let the automatic minibrot-finder do the rest over night to find the minibrot (even if it's not perfect and stops some times) smiley
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Dinkydau
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« Reply #2 on: May 07, 2014, 01:48:28 PM »

Thank you, and I totally agree about the morphing. I think there are only a few people on the planet who do this. When the mandelbrot set was discovered and gained popularity, it was impossible to design shapes like this, so they couldn't be discovered right away. Since then, it looks like the idea has been established that it's certainly a cool fractal and all, but everything is already known. It's not true. I think if the mandelbrot set was discovered today, and perturbation shortly after, many more people would explore. I'm also ignoring similar fractal types by the way. z^3 + c must have equally interesting shapes, just with different symmetries. A lot is possible.

Yes, zooming like that is very fast and efficient and just to make it clear, I wouldn't suggest to take it out. However, it's only really useful if the rendering is so slow (and the depth is so great) that time can be taken to point the cursor right at the center. To start out from zoom level 0, the method like in fractal extreme / mandel machine gives (at least it gives me) more feeling of control over the direction and more speed.

For this render, I first used fractal extreme to experiment with the zoom method, then zoomed to this location in kalles fraktaler (scrolling at first, then by clicking), and then rendered it in mandel machine in I think less than a minute!
« Last Edit: May 07, 2014, 01:56:00 PM by Dinkydau » Logged

cKleinhuis
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« Reply #3 on: May 07, 2014, 02:29:11 PM »

what do you mean with "morphing shapes" using special pathes to create a certain shape !?

and  for z^3 i have the opinion that it does not posess such a variety, but i might be wrong, what about using pertubation theory for other exponents?
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Kalles Fraktaler
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« Reply #4 on: May 07, 2014, 04:11:25 PM »

what do you mean with "morphing shapes" using special pathes to create a certain shape !?

and  for z^3 i have the opinion that it does not posess such a variety, but i might be wrong, what about using pertubation theory for other exponents?
I did not make perturbation work on z^3... sad
http://www.fractalforums.com/new-theories-and-research/pertubation-and-3rd-degree-mandelbrot/
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knighty
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« Reply #5 on: May 07, 2014, 07:43:46 PM »

Super cool Dinkydau!
 Wow
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youhn
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« Reply #6 on: May 07, 2014, 08:17:51 PM »

what do you mean with "morphing shapes" using special pathes to create a certain shape !?

Exactly! Grab a julia as starting point and zoom into "subparts" that are interesting. Further down you'll find a embedded julia, which has properties of both the mother-julia and it's subparts on which you were focussing (zooming). See also topic:

http://www.fractalforums.com/help-and-support/deep-zooming-to-interesting-areas/msg73145/#msg73145
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Dinkydau
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« Reply #7 on: May 07, 2014, 08:43:11 PM »

Thank you!

what do you mean with "morphing shapes" using special pathes to create a certain shape !?

and  for z^3 i have the opinion that it does not posess such a variety, but i might be wrong, what about using pertubation theory for other exponents?
The z^3 set has almost the same properties as z^2. It has minibrots, julia sets, shapes that increase in symmetry, the "valleys" show similar looking patterns... it's only the numbers that are different. The most important difference is the symmetries. In z^2, the symmetries are the powers of 2 (1, 2, 4, 8, 16, ...) while the symmetries in z^3 are the powers of 3 (1, 3, 9, 27, 81, ...). That means you can't find straight shapes like the one this thread is about, because 2-fold symmetric shapes don't exist in z^3. However, the same shapes do exist in the 3-fold symmetric versions. Example:

Consider this shape in z^2:


Doing the same zoom method in z^3 results in the following:
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laser blaster
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« Reply #8 on: May 07, 2014, 08:48:50 PM »

what do you mean with "morphing shapes" using special pathes to create a certain shape !?

and  for z^3 i have the opinion that it does not posess such a variety, but i might be wrong, what about using pertubation theory for other exponents?
It could just be that people haven't explored it enough to find the really interesting bits. It has most of the same basic structures as z^2 (elephants, scepters, double spirals, no needle though), so I'd expect about the same level of variety.

Oh, hey, it looks like knighty just fixed the perturbation formula for z^3 today. Yay. smiley
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