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Author Topic: Introducing the Tanglebrot: Another valiant attempt at the holy grail  (Read 1696 times)
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msltoe
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« on: October 20, 2012, 03:51:38 AM »

The idea of the tanglebrot is that when you are near the root regions of the Mandelbrot (in this case the Juliabrot), permute the coordinates and scale the coordinates. The formulation I've come up to make it somewhat nice looking is a bit of a hack.
Maybe we can find better parameters and/or formulas to work with.
 
Here's the inner loop:

   r=x*x+y*y-z*z;
   if (r>0.01) {
     x1 = (x*x-y*y);
     y1 =     2*x*y;
     z1 =       -2*z*sqrt(x*x+y*y+0.5*z*z);
     x = x1+a; y = y1+b; z = z1+c;
   }
   else
   { x1=z*3;
     y1=x*3;
     z1=y*3;
     x=x1;y=y1;z=z1;
   }
 
« Last Edit: October 20, 2012, 03:53:50 AM by msltoe » Logged
msltoe
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« Reply #1 on: October 20, 2012, 04:37:45 AM »

Another J-set that is a little easier to visualize what's going on:

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matsoljare
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« Reply #2 on: October 20, 2012, 03:51:27 PM »

Can you try this on a Julibrot?
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msltoe
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« Reply #3 on: October 20, 2012, 05:24:42 PM »

Matsoljare, thanks for the request. I think you mean the M-set. The above two were J-brots.
Here's the M-set, not nearly as convincing.



* tanglehoot.jpg (203.13 KB, 1600x1600 - viewed 327 times.)
« Last Edit: October 21, 2012, 09:51:41 PM by msltoe » Logged
matsoljare
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« Reply #4 on: October 21, 2012, 09:23:35 PM »

Yeah, sure isn't convincing at all.... cause it only shows an error message!
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msltoe
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« Reply #5 on: October 21, 2012, 09:52:52 PM »

The M-set picture was in my Flickr photostream. I modified the post and put the image on the forum.
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cKleinhuis
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formerly known as 'Trifox'


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« Reply #6 on: October 21, 2012, 10:07:48 PM »

it is loking nice, a candidate, not much detail, but certainly a candidate containing the mset ... so lets see how the 8th power looks wink
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #7 on: October 22, 2012, 12:12:01 PM »

Lil question;

Is the formula discontinue? wink
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matsoljare
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« Reply #8 on: October 22, 2012, 11:37:57 PM »

Wow, that looks awesome, i'd like to see some closeups, on the middle of the main bulb especially....
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msltoe
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« Reply #9 on: October 23, 2012, 04:10:11 AM »

Thanks guys!

DarkBeam: The formula I've presented is discontinuous, although the breaks are not to so jarring because they occur only when the permutation is made and there is often space between the two segments. I'm working on a C0 continuous version, but I'm not sure if it will pan out.


Christian: Not sure what an 8-th order would mean for this beast given I'm not using a typical spherical coordinate-derived formula. My goal has always been to get the 2nd order to have lots of fractal goodness. I think that when we go up to 8th order with a lot of these functions we get lots of near-conformal regions to feast our eyes on.

Matsoljare: Here's a closeup of the center of the M-set. Looks like navel lint to me: smiley



* navel_lint.jpg (45.13 KB, 700x374 - viewed 324 times.)
« Last Edit: October 23, 2012, 04:46:39 AM by msltoe » Logged
KRAFTWERK
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« Reply #10 on: October 23, 2012, 08:44:05 AM »

Those Julias are beautiful  A Beer Cup
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Alef
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« Reply #11 on: October 23, 2012, 05:18:54 PM »

cutted julia features is nice and used colour method is nice. But probably old formula revisited Bennesi looks more grailish;)
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msltoe
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« Reply #12 on: October 24, 2012, 02:19:39 AM »

One more J-set to put out there. I made the formula more continuous if anyone is interested I'll post the formula.
I call this one "Dragons":


* dragons.jpg (172.81 KB, 1200x648 - viewed 343 times.)
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Alef
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« Reply #13 on: October 28, 2012, 05:01:53 PM »

Discontiniues looks better. Anyway, probably there are smooth surfaces of discontiniuaties, and not mess like Barnsley formula. At least it don't seems mess like Barnsley. Maybe this could be a transform. Like most 3D brots it is fractal in 2 dimensions, just it is more beautifull. A peacock
« Last Edit: October 28, 2012, 05:08:33 PM by Asdam » Logged

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DarkBeam
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« Reply #14 on: January 30, 2015, 10:48:38 AM »

Ack!

Please yes post the continuous version? cheesy
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