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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:

(http://i45.tinypic.com/iwrpci.png)

and a few more:

(http://i50.tinypic.com/2exohub.png)

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  :)

In the Wiki, that should surely be "a^2 - b^2" not "a^2 + b^2" ?

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's basically multiplying the real and imaginary parts separately, along with the normal complex squaring operation. I posted about this here:

http://www.fractalforums.com/mandelbrot-and-julia-set/strange-possibly-unknown-mandelbrot-variants/msg5773

I'd still love to see someone implement my idea of Supermandelbrot/Superjulia rendering, calculating an entire Mandelbrot/Julia set for each pixel and using the number of inside/outside pixels to decide the color.

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

Actually, a mandelbrot set is exactly the same as a "super julia set", so to speak. Every pixel of the mandelbrot set corresponds to a positive-area Julia set. Points outside the mandelbrot set (or at Misiurewicz points) correspond to julia sets with zero area (locally connected or not), and they correspond to the non-white points on the mandelbrot set. See this picture here:

(http://upload.wikimedia.org/wikipedia/commons/8/8e/725_Julia_sets.png)

So as you can see, a superjulia set would look exactly the same as a mandelbrot set.

By the way, my applet code is actually really extensible so I can code for a supermandelbrot set if you really wanted (which would render 262144 times slower than a normal mandelbrot set in the worst case). the problem being what parameters I should take for each point (what does x correspond to? what does y correspond to? etc.) Please give more detailed specifications and I'll cook up an applet for you. If you can advertise my blog a little bit that would be nice too ;)

EDIT> Scratch that, I just realized that the method you suggested would actually allow me to color the interior of the mandelbrot set. I'll work on a render right away.

and this video :)
http://www.youtube.com/watch?v=H603qZfhTNM

For some other formulas though, such as Nova, Newton and Phoenix, this is NOT the case, which was what made me think of this idea in the first place.

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

Kerry

that image looks great :D

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.
 

It got nerfed  :angry: Give it time, if this grows popular, I bet we can get it back on.

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:
(http://i48.tinypic.com/30ry88p.png)

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:
http://www.youtube.com/watch?v=abimf5s9kMI

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:
(http://i48.tinypic.com/xbn77o.png)
Palette curve = 500:
(http://i46.tinypic.com/2m4ogmg.png)
Palette curve = 1000:
(http://i50.tinypic.com/zlrbc9.png)

UPDATE:

Xyrus02 (http://xyrus02.deviantart.com/)was nice enough to host this so that it's accessible by web: No more downloading zip files to run this applet!
http://dl.dropbox.com/u/2426275/xyrus.clan-boa.com/extern/chaosbrot/index.html