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Title: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wolf!!"
Post by: M Benesi on July 16, 2010, 06:01:09 AM
  This new coloring method (calculating 1 more iteration past max iteration, then using the magnitude of all values to assign color) really makes some interesting patterns, especially for good old z^2!  Using an additional iteration in other fractal types will probably be equally as awesome.  Anyways...

Code for calculating fractal (which is also used to calculate the color) is posted after images (although it is a totally standard 3d bulb, although it is the faster complex triplex variety (instead of trig)).

seahorse valley:
(http://lh4.ggpht.com/_gbC_B2NkUEo/TD_gOLhc1BI/AAAAAAAAAk0/siywy0HnaFM/serhorse%20valley.jpg)
elephant valley
(http://lh6.ggpht.com/_gbC_B2NkUEo/TD_V3LVyEhI/AAAAAAAAAkU/XhMkLeqF4NQ/1280%202nd%20order%201000x1000%20elephant%20valley%200%20is%201%20colorinig.jpg)
1 more iteration:
(http://lh6.ggpht.com/_gbC_B2NkUEo/TD_V3VNJnfI/AAAAAAAAAkY/-MQAQ9BGspY/1280%202nd%20order%201000x1000%20elephant%20valley%200%20is%201%20colorinig%20one%20more%20iter.jpg)
17 iteration deep zoom into above 8 or 9 iteration image:
(http://lh4.ggpht.com/_gbC_B2NkUEo/TD_X2XyjZ5I/AAAAAAAAAks/x7rplutcJek/elephant%20valley%20a%20bit%20more.jpg)
zoom on top part:
(http://lh4.ggpht.com/_gbC_B2NkUEo/TD_V3dMvJFI/AAAAAAAAAkc/tof4NoTrsTU/1000%20zoom%20in.jpg)
side view straight on:
(http://lh6.ggpht.com/_gbC_B2NkUEo/TD_V4EDa_yI/AAAAAAAAAkg/adC7xV0Z6A8/1280%202nd%20order%20mandy%20straight%20on.jpg)
side view top down:
(http://lh4.ggpht.com/_gbC_B2NkUEo/TD_V4IYMgbI/AAAAAAAAAkk/53DWqHmDNMY/1280%202nd%20order%20mandy%20top%20down.jpg)

  Anyways, here is the code (from another thread).  It's simply the Mandelbulb formula I prefer due to its simplicity, the fact that it's faster than the trig versions, and the it is an obvious extension of complex numbers.

Code:
	r1=sqrt(sqr(sy)+sqr(sz));
	r3=r1^(-n);   // take it to the -n so you don't have to divide by r3, as it can equal zero for the first iteration

	victor=complex(sx,r1);
	bravo=complex(sy,sz);  
	victor=victor^n;    // for higher powers, set up a script if n= integer powers for each n so
	bravo=bravo^n;   //  for  n=4   bravo^4 = sqr(sqr(bravo))     ||   for n=6 bravo^6 = sqr(bravo)*sqr(sqr(bravo))
			 
	nx=real(victor);
	ny=imag(victor)*real(bravo)*r3;  // since r3=r1^-n you don't have to divide here.. good if r3=0
	nz=imag(victor)*imag(bravo)*r3; 

	if (juliaMode) {
		sx=nx+cr;
		sy=ny+ci;
		sz=nz+cj;		
	} else {
		sx=nx+(pixelr);
		sy=ny+(pixeli);  // take the abs(pixeli) for a more uniform fractal, although the distortion of the even n
		sz=nz+(pixelj);	//  z^2,4,6....  is to be expected considering the asymmetry of the 2d set for even n
	}
	z=quaternion(sx,sy,sz,0);  //this feeds information to ChaosPro's orbital color scheme
                                            // it sends the x, y, and z values to the coloring calculation which simply repeats the above
  // calculation one (or more) time
	bail=abs(sx)+abs(sy)+abs(sz);

(http://lh4.ggpht.com/_gbC_B2NkUEo/TD_2CRp_TlI/AAAAAAAAAlI/5egJNqCcxp4/nice%20colors%20again.jpg)

Title: Re: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wol
Post by: jehovajah on July 16, 2010, 08:32:36 AM
Fantastic Matt! I knew you had colour in you as well as pattern and rhythm :thumbsup1:

Title: Re: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wolf!!"
Post by: ker2x on July 16, 2010, 10:28:49 AM
anyone willing to try on a 2D mandelbrot ? I'm curious :)
(i'm at work right now, can't do it  :sad1: )

Title: Re: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wolf!!"
Post by: kram1032 on July 16, 2010, 11:43:38 AM
that looks nice :D

Title: Re: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wol
Post by: trafassel on July 16, 2010, 02:42:08 PM
Congratulation, it should solve the question, how
to color the surface of the Mandelbulb.

Very good work.

 

Title: Re: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wolf!!"
Post by: M Benesi on July 16, 2010, 07:41:44 PM
Sheesh all,

  I just realized using the regular orbit formula (no additional iterations) does the same thing... basically.  hahaha.

   Anyways, it does look nice.  :D

  Here are some regular orbit (by that I mean same number of iterations as formula) averaged orbital magnitude (averaged x, y and z components individually, so for 10 iterations took all 10 x components and divided them by 10, same with y and z components; then calculated magnitude of averaged x, y, and z components.  note: instead of this, we could calculate orbital magnitude each iteration and then average that).

all z^2:
(http://lh3.ggpht.com/_gbC_B2NkUEo/TECw7UqBE5I/AAAAAAAAAlc/W3zX-BQinBE/help%20im%20glowing.jpg)
zoomed and iterated one more time:
(http://lh3.ggpht.com/_gbC_B2NkUEo/TECw7pFIA5I/AAAAAAAAAlg/j9j7LYAM8cg/glowin%20zoom%201.jpg)
zoomed and iterated a few more times (a couple zooms):
(http://lh4.ggpht.com/_gbC_B2NkUEo/TECw74o0CFI/AAAAAAAAAlo/qA70wkHZvDM/glowin%20zoom%202.jpg)

Title: Re: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wolf!!"
Post by: M Benesi on July 17, 2010, 09:37:02 PM
Another 2 z^2 (next one in 10 minutes or so). z^2 are really awesome looking... just like in the 2d set.

(http://lh5.ggpht.com/_gbC_B2NkUEo/TEIFVud4EJI/AAAAAAAAAl0/oXe15wtay9o/z%20squared%20mandelbrot%20awakens.jpg)

(http://lh5.ggpht.com/_gbC_B2NkUEo/TEIN6Bo2RiI/AAAAAAAAAl8/ejCN02xzPKY/z%20squared%20mandelbrot%20awakens%202.jpg)

Title: Re: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wolf!!"
Post by: jehovajah on July 22, 2010, 06:06:30 AM
So Matt the colour algorithm is new but the specification is simpler. I would like to see what happens when you iterate to a z^2 mandlebulb with mini mandelbulbs along the axis. This certainly brings out the details. ;D

Title: Re: complex compound /w new coloring z^2 looks like a 3d Mandelbrot. "Wolf, Wolf!!"
Post by: M Benesi on July 22, 2010, 08:29:36 AM
  Not entirely sure what you mean Jehovajah? 



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