My application has an option to create 3D Mandelbrot and Julia set fractals using the Distance Estimate Mehtod (DEM), as documented in "The Science of Fractal Images" (and also in the link I provided).

I use the DEM values as the basis for a height map.

For the most part DEM works quite well as a source for height values.

However, for Julia sets centered on the origin, the center of the plot has an annoying spike in the middle (If large DE values are plotted as large height values.) This is because the Julia set DEM algorithm breaks down for points very close to the origin.

Is there a way for me to correct for these errors? I'm not that concerned about a mathematically rigorous solution. I just want a way to get rid of the ugly spikes that mar the middle of my images.

Here are 2 versions of a 3D Julia set plot.

First, and image centered on the origin:


And another Julia set using the same C point. This one is centered on the "C" point (zooms into Julia sets look VERY similar when centered at the origin and at their "C" point.)


Note the ugly spike in the center of the plot centered on the origin. This is an artifact of the breakdown of the DEM algorithm for Z very close to the origin.


Duncan C

Trifox,

Thanks for your kind words. I'm quite happy with the 3D plots overall. As to smoothing around the zero point, I guess that might be possible. I'd need to find a good radius to smooth. The sample plot with the spike in the middle is at a width of 4.15E-3 for the whole plot. I did some further zooming, and I think the spike is around 3E-9 in width, at least for this plot.

I am definitely planning doing 3D animations. Right now I'm recovering from a hard drive crash. Then I'm going to add support for stereo projections of various types, and then comes generating movies.

Your alternating seeds method is interesting. I'll have to play around with it.


Regards,

Duncan