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I don't know if anyone has tried this before, but i've considered a new way of rendering Mandelbrot and Julia sets for any formula that i'm sure have great visual potential.

For each pixel on a Mandelbrot set, instead of rendering just one point and determining the outcome, render an entire Julia set with the values given by the pixel, and use the amount of attracted vs escaping points to decide the color. The same could be done the other way around instead, with a Mandelbrot set being rendered for each point on the plane.

It can also be thought of as "every" Julia or Mandelbrot set (within a limited space and with limited resolution) put on top of each other and mixed.

This would of course be very computationally expensive, but possibly worth the work.

Another variant is where simply a "line" of values are rendered for each pixel. The images below are a very simple attempt at rendering that with a very slow QBasic program, and can probably be done in much better ways.

Perhaps this could be called Supermandelbrot and Superjulia, with the 2-dimensional version being Hyper-ditto?

(http://i161.photobucket.com/albums/t208/oljare/mand_real.gif)

(http://i161.photobucket.com/albums/t208/oljare/mandimag.gif)

(http://i161.photobucket.com/albums/t208/oljare/juliareal.gif)

heya  O0

the method you describe and the results you've shown seem kinda similar to something i did a while back, have a look at these animation: http://fractographer.com/anims/julia2_x264.avi

you'll need the x264 codec (or vlc player), which you can get with the (excellent) ffdshow plugin at http://x264.nl

That appears to be similar, though it might have been more interesting if you had used a regular "black white" rendering instead. I believe those are using "lines" of values rather than the full plane? Though it strikes me you could get the same result by simply making a video of a Julia set with changing values and applying a motion blur effect, which is what it looks like...

I made some experiments in QBasic using a random value for each pixel to spread it evenly through the full real and imaginary plane, and though the result was very noisy, it seems rather promising. I'm sure someone's thought of it before though.

Actually the reason i thought about this in the first place was when reading about some J and M sets for alternate formulas, where it was noted that the Julia set of certain formulas wasn't very related to the Mandelbrot set, so it couldn't be used for a "map" in the same way, and i thought there must be another way to construct a useful map for the Julia sets in this manner.

correct, it is (a form of) motion blur; actually what it is, is a moving time-integral of the julia images produced by a trip around the main lobe of the mandelbrot set against a weird periodic kernel function, so that it forms something of a moving time-derivative. this is computed numerically using monte carlo integration, which is the scientific basis of your qbasic experiments  O0

Here's a variation that works with both inside and outside pixels:  Color by the fraction of times that the real part of z is less than the imaginary part of z at the end of the iteration.  I call this example, "dust storm."   :)

Kerry

That's not bad looking, but what software did you use for this?

It's a coloring formula that I wrote for Ultra Fractal.  When I've finished it, I'll upload it to the Ultra Fractal formula database.  Until then, here's another trial.

Kerry

Wow, that looks like it's burning! Absolutely fantastic!

Thanks!

I'm disappointed that it seems like none of you here are very interested in this. I thought i had run into something really big here....

I think it's a neat idea and have used it in some images. But, you can't tell what will resonate with people when. Just keep working on your ideas and putting them out there--someone will be interested.

The top two images really just look like different perturbations of the m-set superimposed on top of each other. But I understand that is not the way you computed it, so I guess it is just an interesting connection.

Hi
I don't remember what colouring formula I used for this picture, but I just put it here because of graphical similarities.
(http://www.fractalforums.com/gallery/0/492_08_06_09_11_18_34.JPG)

No, that IS exactly what it is supposed to be. But the ones i rendered are only a limited few, while i intend the "complete" (within reason) set of Mandelbrot or Julia sets to be combined.

All right then, I just got confused by the "Rendering an entire Julia set". I think I understand now, though.

Ok, here's a few shots. It sure took a long time to calculate.

Great, i'm sure another choice of palette would bring out the details much better. Be aware that instead of rendering the full plane, you can render a single "line" of parameter values for each pixel. Either real, imaginary or anywhere else.

Hey, didn't I PM you an applet? Link to the screenshots here :P.