Mathematical physics reveal nature's formula for survival (w/ Video)

May 14, 2012 by Miles O'Brien

(Phys.org) -- The vascular system of a leaf provides its structure and delivers its nutrients. When you light up that vascular structure with some fluorescent dye and view it using time-lapse photography, details begin to emerge that reveal nature's mathematical formula for survival.

When it comes to optimizing form with function, it's tough to beat Mother Nature.

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"If you begin looking at them in any degree of detail, you will see all of those beautiful arrangements of impinging angles and where the big veins meet the little veins and how well they are arranged," says Marcelo Magnasco, a mathematical physicist at Rockefeller University in New York.

With support from the National Science Foundation (NSF), Magnasco and his colleague, physicist Eleni Katifori, analyze the architecture of leaves by finding that link to function.

They study a specific vascular pattern of loops within loops that is found in many leaves going down to the . It's a pattern that can neutralize the effect of a wound to the leaf, such as a hole in its main vein. Nutrients bypass the hole and the leaf remains completely intact.

"Something that looks pretty looks pretty for a really good reason. It has a well defined and elegant function. We can scan the leaves at extremely high resolution and reconstruct every single little piece of vein, who talks to who, who is connected to who and so forth," explains Magnasco.

Magnasco and Katifori digitally dissect the patterns, level by level. "It was very hard to get to a unique way of actually enumerating how they are ordered. Then we hit on the idea that what we should do is start at the very bottom, counting all of the individual little loops," recalls Magnasco.

"This research is a unique interdisciplinary partnership in which physics is used to address biological problems, and it is our belief that the mathematical and will play a major role in in this century," says Krastan Blagoev, director for the Physics of Living Systems program in NSF's Mathematical and Physical Sciences Directorate, which funded the research.

Magnasco says this research is a jumping off point for understanding other systems that branch and rejoin, including everything from river systems to neural networks and even malignant tumors. "When a tumor becomes malignant it vascularizes, so understanding all of this is extremely important for understanding how these things work," says Magnasco.

Explore further: Hyperbolic homogeneous polynomials, oh my!

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User comments : 10

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Telekinetic
not rated yet May 14, 2012
Neural networks? Hell, that leaf looked like a human brain! And I wonder when a parallel will be drawn between the living physical structure and consciousness itself, that it might serve as the most efficient transmission of information in all of its dimensions.
simplicio
5 / 5 (1) May 14, 2012
So what is mathematical formula? They did not say. Fractal?
MandoZink
not rated yet May 15, 2012
It didn't look fractal. Too random.
BradynStanaway
not rated yet May 15, 2012
Probably Fibonacci?
ziphead
1 / 5 (1) May 15, 2012
To the article writer; why bother?
CardacianNeverid
5 / 5 (1) May 15, 2012
It didn't look fractal. Too random -Mondo[/q
It doesn't look random to me. It's like the vascular system in animals, bifurcations on top of bifurcations to ever smaller scales. Of course it's not perfectly symmetric, but I think it does exhibit a fractal dimension.
gmurphy
5 / 5 (2) May 15, 2012
It's almost certainly fractal, specifically a branch of fractals called L-systems http://en.wikiped...L-system
MandoZink
5 / 5 (1) May 15, 2012
It's almost certainly fractal, specifically a branch of fractals called L-systems

Could be. The area between veins on many of the leaves in the video reminded me of the Penrose tilings in the WikiP reference.

To the article writer; why bother?

Learning how leaves evolved a method to bypass common injuries and still provide nutrients to continue growing seems to be a damned good thing to me. Why would you be visiting a science site if "why bother" is your outlook?
HTK
not rated yet May 16, 2012
Strange?

Didn't the father of fractal mathmatics already produce the formulas?
HTK
not rated yet May 16, 2012
Look it's definitely fractal benoit betonbrut already been there done that so what's the news???

Benoit should get the credit.

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