What to do about Julia set DE Errors for points close to the origin?

[Duncan C]

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

[cKleinhuis]

those images are fantastic, the hillyness is quite cool,


to the coloring algorithm ... i just know that the dem algorithm is only working fine for the non-julia parts of the fractal

but, i would try tweaking with the julia seed, and, hehe, to make it brute force, you could do a smoothing around the zero point, a gaussian blur of size 0.1 or 0.01 for the area around the zero point,

have you ever thought about animating those 3d fractals ? 

  great work, i love to see so many fractal coders around here

as i heard you are also interested in new ways of rendering ... you should try my alternating mandelbrot method ...

i have written something about it here:
http://fractalmovies.com/index.php?option=com_content&task=view&id=31&Itemid=34

the method is quite simple, just alternate two different seeds in the iteration loop, the outcome is quite interesting, and can be combined easily with many different fractal formulas, but the best thing is that it does not cost extra calculation time, and you can use as many seeds you want, if you want to know more, open up a thread
 

[Duncan C]

those images are fantastic, the hillyness is quite cool,


to the coloring algorithm ... i just know that the dem algorithm is only working fine for the non-julia parts of the fractal

but, i would try tweaking with the julia seed, and, hehe, to make it brute force, you could do a smoothing around the zero point, a gaussian blur of size 0.1 or 0.01 for the area around the zero point,

have you ever thought about animating those 3d fractals ? 

  great work, i love to see so many fractal coders around here

as i heard you are also interested in new ways of rendering ... you should try my alternating mandelbrot method ...

i have written something about it here:
http://fractalmovies.com/index.php?option=com_content&task=view&id=31&Itemid=34

the method is quite simple, just alternate two different seeds in the iteration loop, the outcome is quite interesting, and can be combined easily with many different fractal formulas, but the best thing is that it does not cost extra calculation time, and you can use as many seeds you want, if you want to know more, open up a thread
 

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