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Author Topic: Approaching the holy grail with a scoring system of the like  (Read 1037 times)
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kjknohw
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« on: August 16, 2012, 09:27:36 AM »

What are the properties of the mandelbrot set?
         Diversity: Each area is different.
                      The mandelbox does pretty well. The mandelbulb and tetrabrot seems better though.
         History: When you find a baby mbrot, you see patterns remiscent of everything you passed earlier.
                      I believe that the mandelbox fails this criteria (are there baby mandelboxes), the mandelbulb and tetrabrot passes.
         Not stretched: Detail is found in all directions
                     The mandelbox is perfect here, but the mandelbulb has whipped cream regions. The tetrabrot has long "tubes".
         Connected (less important in my opinion):
                    The mandelbulb/tetrabrot passes the mandelbox sometimes fails.
There may be no perfect grail because of you-know-what theorem, however, why can't the transformations' non-conformity cancel each other out? Or nearly so; for example, the mandelbar/tricorn has in most places a tolerable distortion.

Can there be a way that a score system be developed and the formula "evolve" better and better? Or could we improve our human-based scoring system by looking more closely at these.
« Last Edit: August 28, 2012, 04:48:51 AM by kjknohw » Logged
Alef
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« Reply #1 on: August 26, 2012, 05:09:49 PM »

There must be some judging system to recognise HIM.
But mandelbox is not 3D mandelbrot, becouse 3D mandelbrot must be Z squared what are first requirement for 3D mandelbrot. Mandelbox is something another a pattern formula like 2D ducks/ kalisets.
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kjknohw
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« Reply #2 on: August 28, 2012, 04:56:15 AM »

I don't think HIM will appear suddenly, it will take time and effort or else it would have been found, a true HIM is noble prize material! However, we could tweak the formula incrementally to get closer.
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Tglad
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« Reply #3 on: August 28, 2012, 10:17:08 AM »

Surely there's more variety in Mandelbox than the tetrabrot- https://sites.google.com/site/mandelbox/negative-mandelbox  cheesy

I've got a pet theory that black holes are the grail, and that, rather than being spherical they are somehow fractal-like with infinite surface area.
That is based on zero knowledge of black holes, just a guess!
i.e. rather than it existing in 3d euclidean space, it exists in the massively warped 4d space-time of general relativity.
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M Benesi
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« Reply #4 on: September 16, 2012, 02:56:12 AM »

There are couple z^2 varieties in this thread.

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jehovajah
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« Reply #5 on: September 17, 2012, 04:23:51 AM »

Nice image Matt. What section of z^2 mandelbulb is this?
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mfg
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« Reply #6 on: September 17, 2012, 06:01:38 AM »

When you refer to history, that does not mean that you find small copies of the complete set. Is that right?
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Alef
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« Reply #7 on: September 23, 2012, 06:45:45 PM »

Important condition is that "Holly Grail" should be mathematically meaningfull. Mandelbrot set are, it corresponds to bifurcation diagramm of of the logistic map (throught I have no idea what it means). But some of visualy appealing formulas probably just are not very mathematical.



Anyway I had posted about "Arc of Covenant", 3D fractal what would have natural elements such as fern fronds, coral reefs, trees or seashells. Rotbox hybrid seems somewhat like that item.
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M Benesi
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« Reply #8 on: September 29, 2012, 08:32:38 PM »

Nice image Matt. What section of z^2 mandelbulb is this?
Hey, missed your reply.  It's the "stalk" section- the part aligned with the negative x-axis.  The thread is over in the Mandelbulb theory section.  Don't want to hijack this thread, but this current formula has certain features that others lack.
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