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   Has anyone tried this variation of the Mandelbulb?
 
   r = x*x+y*y+z*z;
   r1 = sqrt(r);
 
   phi   = ( iter*8 )*asin(z/r1);
   theta = ( iter*8 )*atan2(y,x);

   r1 = pow(r,4);
   x1 = r1*cos(theta)*cos(phi);
   y1 = r1*sin(theta)*cos(phi);
   z1 = -r1*sin(phi);

   x = x1+a;y=y1+b;z=z1+c;

 It seems to produce fuzzier versions of the original. Note how I don't accelerate the radial power, just the theta/phi scaling.

 Max iterations = 5, order 8:
(http://www.fractalforums.com/gallery/1/803_10_02_10_6_39_20.jpeg)

 Closeup:
(http://www.fractalforums.com/gallery/1/803_10_02_10_6_19_00.jpeg)

 order 2: "Mandelfrog"
(http://www.fractalforums.com/gallery/1/803_10_02_10_5_30_09.jpeg)

Just a quick tip to speed up your code; instead, do

r = |zri|+zjk^2;
 
phi   = ( iter*8 )*asin(zjk/sqrt(r));
theta = ( iter*8 )*atan2(zri);

r = r^4;

It looks like your doing this (?) ChaosPro, so in the "init" you'll need to set zri=part_r(#pixel)+part_i(#pixel) and zjk=part_j(#pixel). Looks like a big, purple pillow!

The order 2 "Mandelfrog" ist just 5 iterations as well? Strikes me as unusually rich in detail as compared to other order 2 'bulbs.

Really a nice one :D
Just needs more Antialiasing than usual, I guess...
Looksd almost furry :)

Timeroot: My rendering code is just a plain old C program I've written over the last few months.
Hobold: The order 2 moniker is misleading, Only the first iteration has an order 2, after that it's 4,8, ... The net result is of the shape of an order 2 with lots more complexity.
Kram1032: These fractals are slow to render because there's no non-trig form. Anti-aliasing is for those who have the multi-threaded codes :)

Here's a slight variation where the multiplicate factor on the angles is instead 4*(2^iter).

First is the full beast - aliased and all. (Part of the problem is I've resorted to orbit-based ambience for speed)
(http://www.fractalforums.com/gallery/1/803_10_02_10_9_36_00.jpeg)

Next, three closeups using the different schemes: original mandelbulb, iter*8, and 4*(2^iter).
(http://www.fractalforums.com/gallery/1/803_10_02_10_9_28_01.png)
(http://www.fractalforums.com/gallery/1/803_10_02_10_9_29_17.png)
(http://www.fractalforums.com/gallery/1/803_10_02_10_9_30_44.png)

The last one is the fuzziest, but some could argue the beauty of the original.
Finally, the "order 2" with the 2^iter scheme:
(http://www.fractalforums.com/gallery/1/803_10_02_10_7_44_44.jpeg)

Great thingis, i take two of these  ;D ;D


Dont forget: you also need the amount of cores...

The order 2 (and order 8) versions I presented used the z = -r sin (phi) convention.
If you use z = r * sin (phi), instead, the "order 2" fractal is actually pretty good considering that the regular version is pretty bland. Remember, order 2 means doubling the angle on only iteration 1. I think this is another way of approaching calcyman's conjecture, albeit the symmetry of this one looks like a hybrid between regular orders 2 and 4.

(http://www.fractalforums.com/gallery/1/803_11_02_10_4_22_23.jpeg)
(http://www.fractalforums.com/gallery/1/803_11_02_10_4_23_30.jpeg)

Okay, gotcha, C then.

I would like to point out that there are non-trig formulas for these, cos(n*arccos(x)) - if n is an integer - can always be simplified out into a non-trig function. You just need a recursive function of the form multcos(x,n), I think.

Beautiful variaton msltoe!
(http://upload.wikimedia.org/wikipedia/commons/6/6e/Scarabaeid_sal.jpg)


Convenient with the fur @ this time of year, at least here in the northern hemispere  O0

I'd love to see a deeper zoom... always deeper ;)