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Fractal Math, Chaos Theory & Research => Amazing Box, Amazing Surf and variations => Topic started by: DarkBeam on February 08, 2017, 05:27:07 PM




Title: SurfBox - another cool Mandelbox variant
Post by: DarkBeam on February 08, 2017, 05:27:07 PM
I hand-drawn a strange function that I thought could be cool for experimenting with mutations of ABox.
The modification effect is neaty and deserves more deep looking.
Let me show you how it works, just a little tricky formula that adds a fold that will trigger after the normal folding limit to work like an abs() - so the result is something that stays on borderline between Amazing Surf and the old Box!

Code:
        // Mixed fold by Luca 2016.
        // do this for all 3d axis, or 4d axis if you have a 4d abox
        // Tglad normal fold is cfg->x = fabs(cfg->x + fold) - fabs(cfg->x - fold) - cfg->x;
sg = sign(cfg->x);
folder = sg * cfg->x- fold; // fold is Tglad's
folder += fabs(folder);
folder = min(folder, foldModX); // and Y,Z,W
cfg->x -= sg*folder;

If foldMod = 0, you disable the fold of the corresponding axis. Nice to create curly surfaces aka amazing surf ;D
Conversely if foldMod tends to infinity, you get Tglad's fold. I found that 2000 can be enough.
If foldMod = 2*fold, you get the perfect Mixed Folding, simulating abs() and fold at the same time.
If foldMod = 4*fold, you get a double folding just like doing fold twice.


Images on next post. :beer:


Title: Re: SurfBox - another cool Mandelbox variant
Post by: DarkBeam on February 08, 2017, 05:39:01 PM
(http://orig04.deviantart.net/fad3/f/2017/039/7/b/surfbox_by_dark_beam-dayblet.png)

The standard Amazing Box, but with modified folding with value 2. Strange features are already visible in MSet! :D


Title: Re: SurfBox - another cool Mandelbox variant
Post by: DarkBeam on February 08, 2017, 05:49:15 PM
Julia set of coords (0.3333333 ;0.3333333 ; 2) - a point on the critical square. A Julia of a normal ABox of that location looks like a solid cube, nothing else. Like the previous image, this is with all parameters as in the original first Tglad's Abox... minr=0.5 fold=1 scale = 2.
All the parts of this julia are infinitely thin, like Amazing Surfaces. But this formula also has solid parts making it really versatile ... ;)

(http://img12.deviantart.net/f403/i/2017/039/1/c/juliasurfi_by_dark_beam-daybmah.png)


Title: Re: SurfBox - another cool Mandelbox variant
Post by: KRAFTWERK on February 08, 2017, 06:35:49 PM
Hmmmm, looks promising... Great idea Luca!  :beer: O0


Title: Re: SurfBox - another cool Mandelbox variant
Post by: DarkBeam on February 08, 2017, 06:51:57 PM
Thanks Johan, this formula hides many wonders :) :music:


Title: Re: SurfBox - another cool Mandelbox variant
Post by: mclarekin on February 09, 2017, 04:17:34 AM
Looks fast :)  :beer: :beer: :beer:



I recognize that smooth spheric zone :0



(http://www.fractalforums.com/index.php?action-gallery;sa=view;id=19328)

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=19328 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=19328)


Title: Re: SurfBox - another cool Mandelbox variant
Post by: mclarekin on March 29, 2017, 09:39:45 AM
@ DarkBeam

Can you remember if this fold looks like the yellow line on the chart.

So inside the fold limits - no change, then there is a transition , then an offset =  foldModX??


Title: Re: SurfBox - another cool Mandelbox variant
Post by: DarkBeam on March 29, 2017, 04:53:37 PM
Hello! No, my fold is conformal, no angle changes, only sign change in derivates. :) By the way, yes inside the folds nothing happens... Then Tglad fold (without changing the angle, so 1st angle sign inversion), then the derivate changes sign after a while, keeping continuity :dink:


Title: Re: SurfBox - another cool Mandelbox variant
Post by: mclarekin on March 30, 2017, 10:06:26 AM
Fortunately Buddhi always assures me there is no such thing as a stupid question, otherwise  :hmh: :-.  If i had bothered to re-read the post instead of just copying the code and making some guesses I would have realized I was way off :)
 I assumed cfg was the abbreviation for "confusing" lol.

I will have another go and see what i get.

Cheers