dmitri
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    3D Mandelbrot Set
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    From dmitri's personal cargo

    3D Mandelbrot Set


    They call it the "mandelbulb".

    It's the first true 3D representation of the famous mandelbrot set. Here's the classic 2D version zooming into forever for those who don't have a clear idea of what the mandelbrot set fractal is (It's probably familiar to you):

    mandelbrot gif one mandelbrot gif two

    This 3D version has been dreamt about for around 23 years. Rudy Rucker, famous computer scientist, science fiction writer, and Hegel's great-great-great-grandson, came up with the idea in 1987 with a fictional story entitled "As Above, So Below" that's worth a read. It's about a hacker who gets way too fucked up on some kind of hell's angels mystery pill and has a vision of the thing that goes beyond.

    The UFO came lower and then some of the thicker tendrils were brushing against
    me. They felt shuddery, like the metal on a shorted out toaster. I figured the prickly feeling I'd been getting was from invisible fine tendrils that I couldn‟t see. Could it be possible the thing was going to eat me like a Portuguese man-of-war that‟s got hold of a small fish? I screamed out, “Don‟t hurt me, I‟m an intelligent being like you!” and the thing hissed louder, and then suddenly the hissing Fourier-transformed itself into a human voice. A woman‟s voice. “Don‟t worry, William, I am very grateful to you. I wish to take you for a ride.” I tried to stand up then, but I was too fucking zoned. So I just smiled and stretched by arms up to the big UFO ass. UFO? This had to be a hallucination. Slowly, slowly, it came lower. The tendrils were thick as vines, and the fireflies on the tendrils were as big as grapefruits and baseballs. Since this whole ship was a fractal, each of the firefly globs was a three-sectioned thing like the main body: each of them was a dimpled round ass part with a little antennaed head-sphere stuck onto it. This was absolutely the best graphic ever. I was really happy.


    Here's his more recent elaborations on this subject. (Math people, you wanna see this one)

    Check out this gallery of some of the best renders. Lots of nice highres stuff to see!



    I like this Glowing mandelbulb entitled "Hell":



    I'll end this post with some zoom animations. Enjoy!


    Wed, Jan 13, 2010  Permanent link

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    Wildcat     Thu, Jan 14, 2010  Permanent link
    amazingly the first pic of the 3D Mandelbrot set looks eerily familiar, especially since it bears a high resemblance to the manner in which I imagine a future datastream will look like
    TheUndying     Mon, Jan 18, 2010  Permanent link
    Lol, this will sound crazy, but I've had "dreams" of these images. Similar to what Wildcat said about them being futuristic datastreams. When I awoke I could only describe them as algorithms. And the 3D animated "zipper-like" images were also in my "dream." I don't have time to actually read your article just yet, but I will sometime this week, and I'm sure I'll have a lot to say.
    dmitri     Tue, Jan 19, 2010  Permanent link
    Well, if dreams can be regarded simply as consciousness feeding its output data back into its input, that sounds a bit like how a fractal works to me!

    About 6mins in from
    this clip from "The Secret Life of Chaos"    , posted by abhominal here, the mandelbrot fractal equation:



    Watch the above link to the clip for a more visual explanation of what this equation means if you're not mathematically inclined... (Or the whole program if you have the time!)
    TheUndying     Tue, Jan 26, 2010  Permanent link
    Well, I completely understand now. I ended up downloading and watching the full episode.

    Complexity arises from simplicity; order arises from chaos. That's essentially what I got out of it anyway. Chaos theory. I love it. The Mandelbrot fractals (as I now know them to be called) that I perceived in my "dream" were in fact geometric structures that are infinitely divisible. And they can generate some pretty mind-blowing graphics. Pretty sure you posting this has led to a paradigm shift in the way I view reality. I'm new to this stuff.

    dmitri     Wed, Jan 27, 2010  Permanent link
    Glad to hear you're taking all these 'dreams' in as well as everyone should - With thought :)

    The plot thickens...

    Neural activity in the brain isn't a reaction-diffusion process, but there are analogies to Turing's model. "Neurons send signals to each other via their output lines called axons," says Bressloff. Neurons respond to each other's signals, so we have a reaction. "[The signals] propagate so quickly relative to the process of pattern formation, that you can think of them as instantaneous interactions." So rather than diffusion, which is a local process, we have instantaneous interaction at a distance in this case. The roles of activator and inhibitor are played by two different classes of neurons. "There are neurons which are excitatory — they make other neurons more likely to become active — and there are inhibitory neurons, which make other neurons less likely to become active," says Bressloff. "The competition between the two classes of neurons is the analogue of the activator-inhibitor mechanism in Turing's model."


     http://www.math.utah.edu/~bresslof/publications/01-3abs.html 
    Pyxzer     Mon, Feb 1, 2010  Permanent link
    Don't know why, but the last video was a bit frightening. It also reminded me, that I want to see Avatar again.
    bpwnes     Tue, Feb 2, 2010  Permanent link
    I found an Opera widget for exploring the Mandelbrot set

    Mandelbrot II Opera widget
    dmitri     Tue, Feb 2, 2010  Permanent link
    Haha cool, someone else who uses opera!

    http://sourceforge.net/projects/quickman/

    That's a lot funner, though, that widget renders way too slow :/
    dmitri     Thu, Feb 4, 2010  Permanent link
    http://vimeo.com/hubnut/?user_id=subblue&color=00adef&background=f0f0f0&fullscreen=1&slideshow=0&stream=album&id=155683&server=vimeo.com

    There's a video gallery I found with a whackload more animations of this. You can make your own mandelbulb animations with an adobe aftereffects plugin, which also works with photoshop CS4 for static renders:

     http://www.subblue.com/projects/mandelbulb 
     
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