Fractal Quest

[macawscopes]

Hey there, long time reader, but this is my first post, a little mystery puzzle adventure

Late one November evening, as the first snow settled, I found myself gazing far off
into distant regions of the abstract, intermeandering mathematical cosmos.

Using the GPU and memory as a makeshift symbolic antenna, I hacked the computer
into some kind of cyber-mathematical signal transducer. Long into the night, I sat
punching symbol upon symbol into this highly experimental scientific instrument.

Sure enough, out of nowhere a mysterious & intriguing signal popped onto the screen.

"It appears to be some sort of fractal!" I reckoned quietly, in a calm, scientific manner.

Was it only a blob?  A glitch in the tensor?  Whatever it was, it looked strangely
familiar...

Deep inside, however, excitement welled as I dove farther, further into the abstract
mathematical space. I knew what this was. It was none other than a fractal
quest.

Well three months have passed since then, and I've learned more math (and
more computer programming) on this journey than I've ever learned in my life.

Can you identify this strange mathematical entity?

<a href="https://vimeo.com/moogaloop.swf?clip_id=155587929&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">https://vimeo.com/moogaloop.swf?clip_id=155587929&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>

[PieMan597]

It looks like you've somehow found a "true" 3-D representation of the Mandelbrot set, but it is fuzzy.

[macawscopes]

I'm working on writing a paper.  As much as I'd like to share more here, I think I'd better try and get the paper done and on arxiv.org first.