This fractal is called Octic_C. It is a z^8 mandelbrot that I used for some deep zooming experiments back when I was working on Fracton's arbitrary precision math for formulas. This fractal has very thin arms that are a challenge to turn into a 3D model. I was going to try to make this a "perfect" model that faithfully followed the fractal but it proved to be too complex for that to be practical. This model accurately follows the fractal iteration bands at the first few iterations but then the arms get too thin to follow. I could have increased the resolution, but the time to generate the model goes up tremendously at higher resolutions. Even with these settings, the model took 93 hours to generate on my old 2.0 GHz 2 core Power PC Mac Pro that I use for really slow jobs. The 2D image draws in less than 1 second on the same computer so you can see the extra work that goes into making the model. The model has 1.2 million vertices and 1.8 million faces. The 3D image was rendered in Cheetah 3D.

The parameter file for the fractal is:

Octic_C { ; Exported from Fracton.
 reset=2004 type=formula formulafile=fracton.frm
 formulaname=F_20120728_0913 passes=1 float=y
 center-mag=0.2456830297488648/1.076407684405086/25\
 4313154220.581/1/10/0
 params=0/0/0/0/0/0/0/0/0/0 maxiter=100 inside=0
 proximity=0
 colors=000zzzpzzezzWzzLzzBzz0zz0tt0mm0ff0__0TT0MM0\
 FF0880BE0FL0JS0NZ0Re0Vl0Zs0bz6dzDgzKizRlzYozdqzktz\
 rwzlrzelzZgzSazLWzERz7Lz0Fy0Es0Cl0Be09Z07T06M04F02\
 812E22L32S41Z51e61l71s80zE6zKDzQKzWRzaYzgdzmkzsrzp\
 lzmezjZzfSycLy`EyY7yU0xR0rO0kL0eH0ZE0SB0M80F408A0E\
 G0LM0RS0YY0dc0ji0qp0xq6xrDxsKxtRxuYxvdxwkxxryxlwxe\
 uxZsxSqxLoxEmx7kw0hp0ch0Ya0TU0NN0HF0C806806E08L0AR\
 0CY0Ec0Gj0Ip0Kw0Mw7RwFWxN`xVexbjyjoyrtyrtylmyefxZ_\
 xSTxLMwEFw78v00o00h00`00U00N00F00800800E20K50R70XA\
 0bC0iF0oH0vK0vP7wUFw_NxdVxibyojytrytryslxqexoZwmSw\
 kLviEvg7ue0n`0gW0`R0TL0MG0FB0860860DC0JJ0OP0UW0Za0\
 dh0in0ou0pu7qvFsvNtwVuxbwxjxyrxyruylqxemxZiwSevLav\
 EYu7Ut0Rm0Nf0J_0FT0CM08F04804804E05K05Q06W06a07g07\
 m08s0Es7LtFSuNZvVewblxjsyrsyrlymexhZwbSvYLvTEuN7tI\
 0sC0lB0e90Z80S60L50E30720720D50J90PD0VH0`L0fP0lT0r\
 X7s_FtcNugVvkbwnjxrryvryv }

frm:F_20120728_0913 {
 z=pixel:
 zz=z*z,
 zz=zz*zz,
 z=zz*zz+pixel,
 |z|<=4
}

Export Model Settings:

Model Type: Height Field
Grid Samples X 600
Grid Samples Y 600
Min Ext Angle 10.000000
Min Edge Len 0.100000
Min Face Area 128.000000
Model Size X 10.000000
Model Size Y 5.000000
Model Size Z 10.000000
Upper Clamp 30.000000
Lower Clamp 15.000000
Texture Vert: Color Index

Model Statistics:

Total vertices: 1211098
Total faces: 1816549
Total polygons: 49
File size: 94943607
Time 93 hours 0 min 45 sec