All Shapes in One Equation? 74
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."
It's only for shapes (Score:2, Funny)
Yeah, what useless crap. It only applies directly to everything we know in the universe. Such crap! why doesn't it cook me breakfeast?
Re:It's only for shapes (Score:1, Redundant)
No really, it isn't all that useful. If it were somehow applicalbe to partial differential equations, for example, it might offer a simple way of handling many engineering problems.
Granted, being able to describe shapes with a function can be terribly useful, as it might then become possible to use linear algebra or calculus to directly solve various problems relating to that shape's geometry rather than approximatin
sounds familiar (Score:4, Interesting)
This reminds me of the eccentricity ratio, C, of a conic function. It relates the parabola, hyperbola, and elipse. (eg, the parabola is the perfect shape as it has a eccentricity of 1 and the hyperbola >1 while the elipse is 1) However, im curious to what he did to transform a circle into various other shapes, which he did not mention in the article. big secret?
Re:sounds familiar (Score:3, Funny)
Re:sounds familiar (Score:1)
That's what I thought when I read the article. And not for nothing either I think, since it sounds like that's what it's modeling.
Re:sounds familiar (Score:3, Insightful)
Re:sounds familiar (Score:2)
1 - You know this is an exciting article when people are replying to sigs
2 - Socialism: Moderate left-wing totalitarian government, usually post-nationalist, where people smarter than you spend your money to save you from yourself. [Usually has much better slogans than the above, although the phenomenon has not been studied]
Re:sounds familiar (Score:3, Funny)
2 - Thanks. You know you finally found a decent sig when someone replies to it
Re:sounds familiar (Score:2)
Re:sounds familiar (Score:1)
No.
Socialism: an economic system in which capital is controlled by workers (the people who use the capital to get stuff done). Comes in free-market and command-economy flavors. Contrast to capitalism, where capital is controlled by state-designated owners.
It's sad that the legacy of Palmer, McCarthy, and Hoover thrives to the extent that most Ameri
Re:sounds familiar (Score:2)
In fact most Americans seem to think that socialism is the same as communism and that they're both Stalinism. The AC that replied to you earlier is a good example of this sort of retarded world-view.
TWW
Shape eh... (Score:3, Funny)
As an average /.'r I'm definitely out of shape.
Hopefully this will allow me to program a new shape.
One equation... (Score:4, Funny)
now THAT's a nice ring-shape
Re:One equation... (Score:2)
You laugh, but (from the article):
Gielis has patented his discovery, and is developing computer software based on it. Using one formula to produce shapes will make graphics programs much more efficient, he says. It might also be useful in pattern recognition.
On another "note":
References
1. Gielis, J. A generic geometric transformation that unifies a wide range of natural and abst
Shapes are cool (Score:2, Interesting)
So like if it's only for shapes then I'm cool with
it too cause yanno like shapes are cool and stuff.
But seriously,
Bummer. Graphics realism and speed could probably be
greatly enhanced with a technology burned into the
firmware that can make any shape with one equation.
That could be a neat way to do a lot of things. In
the very least it could be a new way to precache
memory if you think about it. Or something.
Yeah so I made it up (Score:1)
I wanted to see who would call bullshit first.
Re:Shapes are cool (Score:3, Insightful)
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
Re:Shapes are cool (Score:2)
Atleaast I can view the paper [amjbot.org] without any subscription.
Also the guy is a botanist, not a mathematician. And the journal he published in is a botanical paper. So I don't think it's surprising that it passed the checks.
Re:Shapes are cool (Score:2)
It's called a "Pentium". It's a highly sophisticated, evolved equivalent of a recursive function. There is rumored to be a number of utilities for it that make it easier to input, output, and compose those functions.
Well i claim prior art (Score:2, Insightful)
Re:Well i claim prior art (Score:2)
It wasn't.
I [snip] wonder why the hell there are so many crappy trivialities being passed off as important research breakthroughs
From the article: "It's a new way of describing nature," and The Superformula might provide a single, simple framework for analysing and comparing the shap
Re:Well i claim prior art (Score:2, Funny)
Re:Well i claim prior art (Score:1)
Re:Well i claim prior art (Score:2)
+1 Funny [!TextBelow] (Score:1)
Re:Well i claim prior art (Score:3, Insightful)
Using one formula to produce shapes will make graphics programs much more efficient,
That means faster and more realistic video games and Sci-Fi/Fantasy movies folks, what could be bad about that?
Re:Well i claim prior art (Score:1)
Ah, but is this necessarily true? Using a single representation may be more elegant or more convenient, in the sense that it allows the creation of programs that allow you to manipulate shapes in "natural" or "intuitive" ways. For the highest performance, it may however be preferable to use an optimized equation for the specific shape that you are drawing.
Re:Well i claim prior art (Score:2)
Yeah but we don't actually know anything about the size or complexity of the formula. That's why most graphics use simplexes to model shapes (ie simplest shape in n -dimensions) like a triangle in 2-D or tetrahedron in 3-D depending on what you need. I can currently model a cube with 12 triangles or 5 tetrahedrons and only 8 vertices, how many would I need with this formula? I'm sure this formu
Re:Well i claim prior art (Score:1)
As someone who as done 3D graphics work, I found the article rather depressing. Getting different shapes based on variations of the circle equation is very old work, and very commonly known (as a child I first read about the idea in a Piers Anthony novel).
And now this guy is patenting whatever he imagines he's discovered. Graphics Gems has some much more clever ideas in every book, and fort
Additional prior art here (Score:2)
Beautiful Shapes (Score:3, Funny)
Ahh...reminds me of when I first got past the Trivia Quiz Age Check questions in Leisure Suit Larry.
What's amazing is that this question was in the 1987 release (no joke):
O.J. Simpson is
a. an R & B singer.
b. under indictment.
c. embarrassed by his first name (Olivia).
d. no one to fool with.
Correct answer: d
Duh.
Re:Beautiful Shapes (Score:1)
What's New (Score:4, Interesting)
--Ben
Re:What's New (Score:1)
http://www.amjbot.org/cgi/content/abstract/90/3/33 3 [amjbot.org]
Patented it? WTF? (Score:4, Interesting)
Call me old fashioned, but I don't think you should have the right to patent maths!
/joeyo
Re:Patented it? WTF? (Score:2)
Bob.
Re: (Score:2)
Re:scary (Score:1)
Think of it as copyrighting his shapes (Score:2)
Java applet visualisation (Score:5, Informative)
bodytag.org/supershapes1/ [bodytag.org]
equation can be found here (Score:3, Informative)
the equation can be found here [swin.edu.au]
(link found on page with java demo linked to in parent comment - thanks!)
Real world? fractals (Score:3, Informative)
I don't know how far this "transformed circle formula" is from a circle formula, but as long as it's an integer-dimension thing, we get nothing from it. It doesn't scale.
The concept of locality is too important - the behaviour of a cell is really parametered by its neighbors; the same ADN is in your brain, your liver and your nails.
Fractals are still a relatively simple method of describing 3D structures - sure it's really hard to start with a real object and map it to a fractal (but Nature works the other way around!). A very small disturbance can create as many shapes as you want; the number of different vegetal organisms showing very similar DNAs seem to support this.
Re:Real world? fractals (Score:3, Insightful)
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 [triumf.ca]. 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 abou
Re:Real world? fractals (Score:1)
Hmm, he just now discovered fractals???
I can still remember back in the days when I would spend countless hours watching a 386 render a fractal in Fractint.
I would always show off all the cool (prerendered) images to my friends. The first thing that most people seemed to say is "kinda looks like a plant growing".....
SuperGlueBooger
stop the presses (Score:5, Funny)
After avoiding the subject for decades, a Belgian biologist discovers mathematics. One of the first areas he plays around with is "polar coordinates". "I never knew math could be this much fun", the biologist is quoted as saying. In his enthusiasm, the befuddled biologist decided to patent several formulas, following a recently fashionable trend of patenting the obvious.
Compression? (Score:1)
Homepage link (Score:1)
P.S.: I find it somewhat amusing that the fortune quote at the bottom of the SlashDot page I'm using to engter this happens to be
"Confound these ancestors.... They've stolen our best ideas!" - Ben Jonson
More technical information (Score:3, Informative)
It describes the superformula as a "generalized superellipse equation". The 3D version is based on superquadrics.
My God! (Score:1, Redundant)
Re:My God! (Score:2, Funny)
My favourite quote (Score:4, Interesting)
But my favourite quote, from his homepage, is:
So... a guy who specialises in finding new ways to help bamboo propagate- and mind you, bamboo is pretty prolific on its own, don't let that 'lucky bamboo' (which is not actually bamboo, but a plant of another type entirely) fool you- has now found a new way to describe shapes. Yes, this is important, but it's not the next big thing. Folks have been trying to find ways to describe shapes by equations in images long before this, and while his rush to patent may cause some interesting snarls up ahead, i find it unlikely that he even understands Fermat's last theorem,
let alone knows the solution and has described it in shape-description formula format.But if he does, he'd better post something more mathematical on his website, because he's just landed himself into mathematician waters- and it's sink or swim there, buddy. You don't get to try it again next growing season (Andrew Wiles' revisions notwithstanding), and contrary to what laypeople tend to believe, they still require proof when you walk in and say something crazy like 'Pi is 3.' [smc.edu] Even mathemeticians are still arguing over the proofs available. And it's pretty cutthroat, with ten-day conferences, [ams.org] so i bet he's in for some entertaining phone calls.
Re:My favourite quote (Score:1, Funny)
Well done!
Re:My favourite quote (Score:2)
Here's how the saying goes:
Don't be so condescending... (Score:4, Insightful)
In related news... (Score:2)
The theorem takes a natural value as parameter n, and n more parameters between 1 and 27. Then, you read out the theorem by replacing each parameter by a letter between 'a' and 'z', and space being 27.
The really interesting point is that every known theorem, including Godel incompleteness theorem and general relativity are special cases of this theorem.
Ok, I'll agree that writing out mathematical symbol is a bitch with it though.
Apple II (Score:1)
I r
Formula wanted (Score:2)
rewrite the oop books (Score:1)
hamburger equation (Score:1)
that uses a parametric equation to draw a
hamburgers. The equation is basically:
X = sin(tan(t))
Y = cos(t)
10 REM HAMBERGER DRAWER - VERSION 1
PRINT " 1 - Hamberger"
PRINT " 2 - Hogey "
PRINT " 0 - quit"
INPUT " Enter Choice:"; chc
IF chc = 1 THEN fat = 170
IF chc = 2 THEN fat = 80
IF chc = 0 THEN GOTO 9999
SCREEN 12
CLS
FOR T = 0 TO 6.32 STEP
x = 300 + 230 * SIN(TAN(T)) 'calc x X = SIN(TAN(T))
y = 225 + fat * COS(T) 'calc y Y = COS(T)
Re:hamburger equation (Score:1)
I did this 20 years ago on a ZX Spectrum (Score:1)