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Author Topic: Extract mathematical formula from Mandelbulb  (Read 3609 times)
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grasshopper
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« on: February 24, 2013, 04:07:55 PM »

Hello,

I'm new with both Mandelbulb and fractals in general and this is my first post. I have been tinkering with Mandelbulb 3d and it's a really great program because it lets me rapidly view and design fractals. The problem, is that when I have a 3d fractal design that I like, I would like to know which formulae give rise to this fractals. They seem to be implicit in parameters of the formula dialogs, but I don't know how these parameters combine to give formulas.

Thank you
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grasshopper
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« Reply #1 on: February 26, 2013, 01:09:29 PM »

Anyone have a clue?

I have found this page:

http://www.fractalforums.com/theory/summary-of-3d-mandelbrot-set-formulas/

with a set of formulas explained. Is there a page with the other formulas contained in Mandelbulb explained?
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cKleinhuis
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« Reply #2 on: February 26, 2013, 01:15:17 PM »

hello, you want to extract the single formulas, or you want to extract the exact image you have created in mandelbulb3d ?

the link you posted is very nice and explains nicely how the mandelbulb math is defined

this math is then used to create other formulas, that are hard-wired into mandelbulber, for a betterunderstanding: the link you posted defines an algebra, defining an +/- and */division operation, with this operations new formulas are build, variants of those formulas are as said before hard wired to the program, and the program uses even more different functions, so the only way to extract the formulas used is to directly download the source code of the program and examine the source code, for another understanding you can try to search the formula names here in the forums, because before they where included in the program they usually have been discussed here in the forums!
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DarkBeam
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« Reply #3 on: February 26, 2013, 02:00:50 PM »

I did not have the time to write down all but some are already explained - press i button on formula tab!

They are coded in assembly and no - you can not extract anything in any way unless you are able to disassemble them! wink But they are structured as an EXE file.
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grasshopper
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« Reply #4 on: February 27, 2013, 12:01:27 AM »

Well I'm a newbie and I'm not sure of the following, but I think the 3D models are constructed by operating several formulas in succession. Hence what I wanted to extract was not one, but the set of formulas that render the fractal.

Quote
I did not have the time to write down all but some are already explained - press i button on formula tab!
Some infos are descriptive  sad while others are mathematical which is what I was looking for  smiley

Quote
so the only way to extract the formulas used is to directly download the source code of the program and examine it
You must be joking, is that really possible?

Would coding a console of some kind with the mathematical background be asking too much?  embarrass

Thanks you all!
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DarkBeam
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« Reply #5 on: February 27, 2013, 09:36:43 AM »

The structure of MB3D is entirely performance oriented. In this logic Jesse thought that a "raw" coding of formulas using the floating point assembly instructions, and sometimes MMX packed instructions, was the best. So we programmed everything directly in assembly that gives a great performance. Too bad, this can be somewhat hard to translate in a math formula ... And some formulas required a trial-error process so original math expression was not good. smiley

That's all - But please ask here what you need to be explained and maybe one day we can fulfill the request. A Beer Cup
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cKleinhuis
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« Reply #6 on: February 27, 2013, 09:54:28 AM »

 i would love to have a description of the menger sponge formulas, and how they look in escape time approach, i know they are somehow distance based equations, but since it is possible to incorporate them in the mandelbrot process through iteration i would like to have a escape time function for it,
e.g. in ultrafractal notation  embarrass
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DarkBeam
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« Reply #7 on: February 27, 2013, 09:56:42 AM »

Hey; you should look in the IFS fractals sections, Kaleidoscopic escapetime IFS... grin

I made it sticky because I learned lots of stuff from here! A Beer Cup
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JosLeys
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« Reply #8 on: February 27, 2013, 10:29:24 AM »

I have also been looking in vain for the code used for the formulas in M3D.
I think it is a great program, and I admire it a lot, but it is too much of a black box for me, as I like to understand what the formulas do.
In particular, I have been looking for the exact code used in FoldIntPower, as this formula gives such great results in combination with the Mandelbox.

Is there anywhere I could find this code?
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DarkBeam
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« Reply #9 on: February 27, 2013, 10:35:13 AM »

Well! That formula is currently included in Fragmentarium as a full script, some its of abox + one or more of foldint, that gives "spudsville" fractal... grin If I remember correctly the formula is

x = abs(x+fold) - abs(x-fold) - x
y = see above, y = see above grin

(but refer to the one found in Amazing Box description as my memory is labile)

then, simply do an iter of power 2 Mandelbulb then multiply z by a customizable factor (somebody uses values like 100) grin
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cKleinhuis
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« Reply #10 on: February 27, 2013, 10:43:10 AM »

ah thanks, i always wonder, since when are escapetime ifs known, and who was responsible for inventing it ?!?!?! huh?
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DarkBeam
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« Reply #11 on: February 27, 2013, 11:02:52 AM »

ah thanks, i always wonder, since when are escapetime ifs known, and who was responsible for inventing it ?!?!?! huh?

of course... Knighty. wink
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JosLeys
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« Reply #12 on: February 27, 2013, 11:14:15 AM »

On FoldIntPow :

In M3D what is the 'R-fold' parameter?

So does it do a box fold first,(what size box?) followed by a sphere-fold (with a large R and a small R, or just a large one?), and then the bulb?
...or is there no sphere-fold?
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David Makin
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« Reply #13 on: February 27, 2013, 12:47:25 PM »

of course... Knighty. wink

Escape -time IFS - I think R.C. Hart and others....

KIFS - Knighty wink But the K is for Kaleidoscopic, not Knighty !!

There are 2D and 3D formulas for escape-time IFS in my collection for Ultra Fractal - in the UF formula database:

mmf4.ufm:3D IFS and mmf4.ufm:Escape-time IFS

However these are "complete" i.e. the algorithm renders the "strictly correct" attractor. KIFS are a subset where the traversal of the IFS tree is somewhat restricted - similar to RIFS (Recurrent) and LRIFS (Language Restricted) but more based around bailout testing than conditional inclusion/exclusion.
Though the two formulas are slightly extended to be RIFS as they do allow some control beyond the plain IFS - restriction on repeats (of given transform), restriction on given depth etc.
« Last Edit: February 27, 2013, 12:57:48 PM by David Makin » Logged

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cKleinhuis
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« Reply #14 on: February 27, 2013, 12:56:08 PM »

great, the thread is really nice, and i just made a 2d ultrafractal variant of it, the folding is really nice and simple!!!
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