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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:


 Closeup:


 order 2: "Mandelfrog"

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

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)


Next, three closeups using the different schemes: original mandelbulb, iter*8, and 4*(2^iter).




The last one is the fuzziest, but some could argue the beauty of the original.
Finally, the "order 2" with the 2^iter scheme:

The order 2 (and order 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.

Beautiful variaton msltoe!



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

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