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."

Comments

sounds familiar

[ddd2k]

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? ;-)

Shapes are cool

[Sevn]

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.

What's New

[frantzdb]

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

Patented it? WTF?

[MacJedi]

WTF? He found an equation that can describle all kinds of fundamental shapes and he PATENTED IT?!

Call me old fashioned, but I don't think you should have the right to patent maths!

/joeyo

My favourite quote

[SolemnDragon]

He specialises in Bamboo BioTechnical Rearch?

But my favourite quote, from his homepage, is:

"Moreover, well known equations from mathematics like the Theorem of Pythagoras, the equations for conics and conics sections and the equation from Fermat's last theorem, are all special cases of this formula."

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,

Cubem autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere.
Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caparet.

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.