Here is a highly zoomed in movie flying through the 3D model in the top image. I changed the color of the bottom iteration bands in the texture map to better show the detail in the model which you can see in the final frames of the movie. Note that in most browsers when the movie is targeted, you can use your arrow keys to single step frames of the movie. See this page for a comparison of models generated using a grid versus this improved method.

There are several more things that can be done to further improve the image. The green stripes visible in some of the vertical walls are caused by projecting a 2d texture map with square pixels onto a model with curves. Changing the model to use the color map directly to color the triangles instead of using a 2D texture map will fix that issue. That capability is planned in a future version of Fracton. There are a few minor flaws visible in the edge when zoomed in. The last frame of the movie shows a few that you can see in the wall of the circular hole in the center of the image. I think the problem is related to the edge search accuracy I chose for this image. Choosing a higher search accuracy should make that go away.

Here is the par file used to generate the fractal and texture map.

halley_jjp { ; Exported from Fracton.
 reset=2004 type=formula formulafile=fracton.frm
 formulaname=F_20101016_1116 passes=1 float=y
 center-mag=0.4115234375000001/0.002148437499999963\
 /0.8533333439999999/1/-90/0
 params=7/0/0/0/0/0/0/0/0/0 maxiter=100
 proximity=0
 colors=UzJ<2>znP<1>B`3<4>H1C<3>i6X<2>znP<237>znP }

frm:F_20101016_1116 {
 ; Type: Halley
 ; From Computers, Pattern, Chaos, and Beauty by Clifford Pickover
 ; See p277 for a related image and formula derivation
 ; Formula and par by Mike Frazier, public domain
 z=pixel:
 lz=z,
 f=z^(p1+1)-z,; Function z(z^p1-1)
 f1=(p1+1)*z^p1-1,; First derivative
 f2=(p1+1)*p1*z^(p1-1),; Second derivative
 z=z-2*f*f1/(2*f1*f1-f2*f),
 abs(|z|-|lz|)>=0.01
}