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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."
Changing one term in the formula varies the proportions of the shape - moving from a round circle to a long and skinny ellipse. ;-)
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?
Great Atrocit
As an average /.'r I'm definitely out of shape.
Hopefully this will allow me to program a new shape.
One equation to rule them all, one equation to find them one equation to bring them all and in the darkness bind them...
now THAT's a nice ring-shape
__________
Love conquers all... except CANCER
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.
The full text appears not to be available online. All of the examples look like simple polar functions. I find it hard to believe that someone discovered a fundamentally new equation for r(\theta).
--Ben
Call me old fashioned, but I don't think you should have the right to patent maths!
/joeyo
2^5
I have a java applet online that allows you to fiddle with the values in the equation and generate the 'super'shapes in realtime:
bodytag.org/supershapes1/
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.
Besides the biologist's own homepage, there is also the Genicap homepage, featuring a link to a PDF whitepaper.
It describes the superformula as a "generalized superellipse equation". The 3D version is based on superquadrics.
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.' Even mathemeticians are still arguing over the proofs available. And it's pretty cutthroat, with ten-day conferences, so i bet he's in for some entertaining phone calls.
"I'd say 'Have a good time,' but arson is still illegal.
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