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All Shapes in One Equation?
asadodetira writes ""One simple equation can generate a vast diversity of natural shapes, a Belgian biologist has discovered. Nature has the story. "The Superformula" sounds impressive, apparently its only for shapes, i thought you could solve lots of PDE's or tensor integrals or something with this, but not, it's only for shapes."
For gods sake, a stupid little Qbasic program i wrote years ago could ALSO generate a lot of different shapes like those using modified circle equations. I called it a "2d renderer" and didnt think it was anything significant. I still dont think it is of any significance and wonder why the hell there are so many crappy trivialities being passed off as important research breakthroughs.
Ever saw the "flower" visualization thingy for winamp?
Its the same thing!
Look, you can plot the graph of a function on a typical 2D cartesian X,Y reference frame or you can plot it in a circular reference frame where Y is the distance from the center at which you plot and X is the "degree" where you plot it.
So if you plot a constant C in the 1st ref. frame you get a straight horizontal line at Y=C and on the 2nd one you get a straight circle where the radius = C.
If you plot a function, like a sine, it will make a wavy pattern along a line, or along a circle - RESEMBLING FLOWERS - like the winamp vis plugin...
This is a trivial mathematical fact and less innovative than the crap MS spews out every other year. Does anyone know where I can read the stupid paper without subscribing to that site?
He added a varying radius instead of a constant one and felt very manly about it. Woop-dee-doo.
The first thing I thought when I saw this article was, "sounds like this guy has discovered fractals". What he's describing would appear (from the limited information provided) to be a fractal equation. It will be interesting to see how easily it is incorporated into Fractint. Fractint currently has about 70 or so different types of fractals that you can tweak, play with, and zoom into to your heart's content.
There is a lot of cool art on the fractint homepage as well as come descriptive information about fractint and the history of the program, which is currently on version 20.0. I've been playing with the program off and on for about 8 years I guess, and think it is the best fractal generator out there.
For those of you not running DOS, try XFractint. The program has a funky install (imo) but works.
What appears to be 'news' about the discovery mentioned above is that the equation is supposed to generate pictures related to 'natural' shapes. I don't really see it so much as being news, as many have noticed that most natural objects have a fractal dimension to them. Trees are the most obvious example. One of the fractals that Fractint will generate is a cool picture of a fern leaf. If you choose type=ifs, and fern for the IFS subtype, you should be able to display it.
Someday, someone is going to find the correct fractal equation for the universe itself. It will probably be about 50 or so characters long. The physicists(sp?) of the world will look at that, then at the huge volumes they use to attempt to describe quantum mechanics, and say "Doh!"
This is an ex-parrot!
I can decide which comment to reply to so I'll just top-level post. Yes, polar coordinate equations are quite simple, and yes, there is prior art for a variety of shape generating equations (for example, superquadrics)... That being said, the fact that this research has been published in Nature is indicative that his work has generated at least *some* excitement among mathematicians. Sometimes the most compelling mathematical constructs are also the simplest. e=mc^2 anyone?
So long, and thanks for all the Phish