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EDIT2>YAY LINK:
http://dl.dropbox.com/u/2426275/xyrus.clan-boa.com/extern/chaosbrot/index.html

I got bored and developed my own fractal renderer one day, and eventually I stumbled upon a broad set of fractals, which I proceeded to name Chaosbrot. While the "chaosbrot" fractals themselves are not the most attractive, their corresponding "Julia sets" are.  Here is a quick render with seed value -0.28125 + 0.849609375i and chaos value 1:



and a few more:



So if anyone wants to test out the chaosbrot fractal series, you can get it from here:
http://www.mediafire.com/file/u1jmmmmj4ob/Chaosbrot.zip

It's a 10KB download from MediaFire.  Instructions for use are in the .ZIP file.  Need Java-enabled browser (and preferably a screen with resolution bigger than 1024 x 768) to run applet.

P.S.  Yes, I know it only renders in blue at the moment, but I have a beta that is extensible for other coloring palettes.  Anyone who wants it should pm me (or post a request on the blog).  Thanks.  Feedback would be appreciated  

Yeah, I fixed it; I was in a hurry to write the article so I forgot that removing the "i" necessarily requires negation before the b^2 term after squaring. Thanks!

It was your post no. 1000 on FractalForums. CONGRATUATIONS!!!

and this video
<a href="http://www.youtube.com/v/H603qZfhTNM&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/H603qZfhTNM&rel=1&fs=1&hd=1</a>

I coded the Supermandelbrot set for Ultra Fractal about a year ago.  It's in the formula database in lkm3.ucl.

This image, http://www.kerrymitchellart.com/gallery21/heavyweather.html, was created using the Supermandelbrot coloring and was featured in New Scientist magazine last November.

Kerry

It appears that this Wiki entry may not be around much longer if it does not get any non-Delete votes.


Thanks for the link and making your four Java SE 6 .class files available for others to try out.
 

I got back to this thread after forever and decided that I might as well just give you guys the developer version I have. I made a quick 10-minute patch to make the beta less memory-leaky and now the UI should be much better and give superior rendering options.

Download link: (.zip is also attached to this post)
http://www.mediafire.com/file/w5kauyzrojk/Chaosbrot%202.zip

Screenshot:


See the "real offset"/"imaginary offset" boxes? It's the same thing as the "perturbations" option on the applet in this link:
http://edgrenweb.se/mandelbrot/

Which was used to make this:
<a href="http://www.youtube.com/v/abimf5s9kMI&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/abimf5s9kMI&rel=1&fs=1&hd=1</a>

Sadly, their applet sucks massively in aesthetic coloring and fractal aliasing, and is really limited, so I added the option to mine.

Coloring algorithm:
-Primitive cycle: Blue/yellow. Emphasizes high contrast,
-HSV escape: Plots HSV value based on what the point's value is when it escapes. (I use a circle of radius 100 as the escape boundary) Hue = argument, saturation = ratio of (iterations required to escape)/(max iterations), value = (modulus - 100) / 100. Mathematically the superior mode of rendering for visualization, but not so much graphically appealing.
-Red/Blue/Green: Colors based on the ratio of iterations required/max iterations. To improve contrast in a region that's too blue, use "palette curve" to set a minimum value of iterations beneath which everything will be colored black.
-Cyclic blue: I find it hard to explain. Let's just say that it's a very good mode of rendering for regions of the set where iterations required vary significantly.

As for what "palette curve" actually does... I'll let pictures do the talking.

With iterations set at 1600:

Palette curve = 0:

Palette curve = 500:

Palette curve = 1000: