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"Mandelbulb," a 3D Mandlebrot Construct, Discovered
symbolset writes "Many know the beauty and complexity of the Mandelbrot set. For some years now a few enterprising mathematicians / rendering fiends have been seeking a true 3D Mandelbrot set. A month ago a solution was found, and it is awesome to behold."
What are they trying to do, make up some 3D fractal that just looks like the mandelbrot? This mandelbulb seems pretty arbitrary, and the whole point of the story seems to be that they've found a good one, not that they've found any kind of "true" solution.
I imagine if they included Mandelbrot fractals as something you can roll up in Katamari, then there would no longer be ANY need to experiment with psychedelic drugs ever again.
If that's the case, it's been a sad day since at least 1984. These things teach us interesting things about numbers and are interesting in and of themselves. As a way of making math more visually beautiful they also serve to draw the interest of youth to a field ordinarily seen as dry and boring.
Help stamp out iliturcy.
I love how ontopic your signature is.
"linux is just DOS with a UNIX like syntax" -- Galactic Dominator (944134)
Also, trying to extend the Mandelbrot set to 3D is ill-defined as there is no good 3D algebra equivalent to the complex numbers (two, 1 and i) or quarternions (four, 1 and i, j, k) - hence you can't express the iteration formula in 3D.
I was following the fractalforums thread for a while, and IIRC that is what a lot of the discussion focused on - "how can we define the squaring operation in 3D such that the Mandelbrot iterative equation gives us something like our vague notion of what we want the Mandelbulb to look like?"
Site is down, but I got an email notification from fractalforums a few days ago, and they had some incredible results. The pursuit is at least as much aesthetic as it is mathematical, and in that respect they've succeeded marvelously.
Remember the film, Jurassic Park? They applied some simple math to make flocking behavior in their dino models look realistic. It works - just about everybody says the dinosaur flocking looks just like real flocking. Of course real biologists who have been trying to find the math behind real flocking have tested those equations the film makers used, and found some trivial little problem like you need to have faster than light telepathic communication between animal brains if you don't want the animals to get into a ridiculous gridlock once you add in some real environment modeling, but it sure looks like it's real flocking.
And I'm sure we'll get paramecium models or mitochondrion models, or whatever, which 'look just like' the real thing, but turn out to be built on math that has fundamental problems with the rest of reality and uses some cheap hack like omitting surface roughness or gravity to gloss over that part, many times before anyone gets an actual model. We'll see 'accurate' models of atomic nuclei that build all 13 stable elements (or all 1047). 'Accurate' models of natural selection that show only plants should evolve eyes will follow. Eventually, your sea slug will act just like a real one does when the liquid it swims in is molten Sodium, (but not, unfortunately, in water).
People will probably work some or most of these out. Accurate computer modeling of some events has happened, and many more will probably happen with advances in technology. Claiming that all of them will definitely work makes about as much sense as claiming all computer based aircraft models can safely skip the wind tunnel test stage of development.
Who is John Cabal?
Ice Cream From Uranus? In accordance with that very popular rule of the Internet... there is another picture for that... a more illustrative one too.
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Man, you must be a hit at parties.
It is not the retina that sees but the visual cortex. So I wouldn't laugh too hard.
but do you even had computer in the 4 digit era? or was slashdot some sort of paper mail based discussion forum?
Gawd, don't they teach you brats anything in school these days? It was all vacuum tubes back then. Of course, it's all ball bearings, now. We would've _killed_ for ball bearings back in the day!
But most people have two eyes, and the parallax between them gives the third dimension.
The Tao of math: The numbers you can count are not the real numbers.
Good point. Hamilton was working on multiplying triples when he discovered the quaternions. Perhaps it can't be done in a sensible way.
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You don't even need a second eye, or at least, you don't need a parallax between them. Simply focusing on an object gives a good idea of its distance. To bring an object at a certain distance into focus, the eye muscles must contract "just so", allowing an estimation of that distance.
An then of course there is our brains, which interpret what we see. This is the reason why we can still have the illusion of 3D when looking at a truly two dimensional picture or TV screen. Of course, we can also be fooled, for example by cartoons or diagrams, into seeing 3D where none truely exists.
Our eyes really are designed to see in 3D. The grandparent appears to be suffering from chronic smartalecitis.
May the Maths Be with you!
No matter how many eyes you have, or where they are placed, you still see only surfaces.
That's interesting. As I think about it, I wander over to my aquarium and stare pensively. The water looks clean, the guppies seem as happy as guppies get. The seaweed is wafting gently back and forth. But wait, do I really see my aquarium? Or am I only staring at its surface?
Suddenly seized by philosophical doubts, I hold my hand in front of my face. Can I see my hand? —or only my palm?
Your remark is similar to one made by the British philospher G.E. Moore, in a paper published some time in the 1940s (I think). Can't remember the title at the moment...might have been "A Defence of Common Sense".
Great men are almost always bad men--Lord Acton's Corollary