Slashdot Mirror
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."
Yeah, what useless crap. It only applies directly to everything we know in the universe. Such crap! why doesn't it cook me breakfeast?
Liberty.
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
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.
For every annoying gentoo user, are three even more annoying anti-gentoo crybabies. Take Yosh from #Gimp for example.
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.
And you know it.
But that's some good bullshit so MOD THIS UP
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
"The Superformula is a modified version of the equation for a circle."
"Gielis has patented his discovery, and is developing computer software based on it."
well, thats more than a little bit scary. i didnt know formulas could be patented. is this something new, or am i missing something?
Gyrate Dot Org - "Where high-tech meets low-life"
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/
I doubt we can do anything with that formula to express Nature's art. Sure, we can build simpler graphical engines, but that's it.
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.
But I'm so fucking BORED!
I wanted to see who would call bullshit first.
For every annoying gentoo user, are three even more annoying anti-gentoo crybabies. Take Yosh from #Gimp for example.
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.
I was doing stuff like this on my TI-85 in 9th grade (5+ years ago). How the heck does this guy get a patent on something so obvious that an only moderately advanced 9th grader could figure it out? I'm sure lots of young students have tried varing the terms of various equations to see what happens. What's the patent number, and what exactly does he claim?
A solution to the problem with music today
Could this possibly be applied to that story from the other day about the more something compresses the better the odds it was produced in nature? And would it still be the image of the object, or could the formula expressing it somehow be compressed? I would assume it would already be expressed in it's simplest form. Hell, what do I know? I count boxes.
Someone hates these cans.
Homepage describing the discovery (which I am still a little skeptical about): Geniaal.be (translated: "brilliant.be")
:-)
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
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.
m
testing out my trending skills
He's discovered the Spirograph!
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
I've just invented a new universal theorem. It goes likes this :
;-)
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.
He invented those shapes, nerds were tiling their bathrooms with them. I don't see why he shouldn't be able to gain royalties from commercial exploitation of his idea. Patenting vs copyrighting is immaterial--isn't he simply protecting intellectual property?
blarg.
A superformula? He must be dividing and multiplying by 0! Damn him! He stole my formula!
It all comes down to the value of 0, you see.
And dividing by 0.
And the interpretation of the infinities that will let Australia launch a rocket. And 0. It's all about 0.
I'm almost certain (this was like, over 15 years ago) that I discovered this same exact thing while experimenting with graphics on an apple II. Using sin and cos left something to be desired speed wise, so I used a completely integer algorithm I found in an issue of sync (the Sinclair magazine!). Then I tweeked it. I also was trying to do 3D, so I tried to make elipses and then elipses with perspective. Not knowing a thing about how 3D graphics were done, matrix equations, etc, I just messed around.
I remember getting some really crazy spiro-graph like images just from a really simple formula.
I'm sure I still have it on a 5.25" floppy, somewhere...
-- Senior Software Engineer, Attorney appearance services, locallawyerapp.com.
How the **** to you patent a formula?! That's the dumbest thing I've ever heard of! Hmmm, let's just patent something that describes a circle or a square.
Obviously something's wrong with patent law.
the equation can be found here
(link found on page with java demo linked to in parent comment - thanks!)
I have always wanted to know the formula for an egg shell...
It's Christmas everyday with BitTorrent.
This is going to ruin all those OOP textbook examples that show polymorphism on multiple shape sub-types. There is no longer multiple "types" of shapes, just parameters to a single shape equation :-P
Table-ized A.I.
Here is an old "hamburger drawer" G-BASIC program
.0006 'define loop
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)
PSET (x, y), 16 'plot point
NEXT T
GOTO 10
9999 END
Table-ized A.I.
I seem to remember the circle command would erroniously take an extra parameter which would make these sort of shapes. Sort of like a Spirograph.
No sharp objects, I'm a programmer!
Does/Can he actually prove that it generates every shape? It's slashdotted already. Such a sweeping statement should be backed up by a rigorous mathematical proof otherwise it would be less misleading to say "It generates many useful shapes"
The paper was not published in Nature. If it had been I doubt many ./'ers would have been able to understand it :) It ws actually published in the American Journal of Botany.
The Nature connection is that it was reported in Nature Science Update, which is a science news service aimed at a general audience. NSU is owned by the same folks who own Nature, but editorially it's independent. It's basically an online science newswire. (I know, I work here -- hence anonymity)
Also, at least in the UK, you can't patent a mathematical formula or algorithm