The Math of Natural Beauty

by Jennifer Frazer on March 25, 2010

Could not resist re-posting this short movie from Bioephemera lest anyone miss it. I love, love, love the music.

I also love the way natural patterns are repetitive*. Similar patterns pop up in the oddest places. Look at the Charter Oak on the Connecticut quarter

and you’re looking at the search pattern of a feeding plasmodial slime mold (a giant ameoboid eukaryote), Physarum polycephalum,

http://www.flickr.com/photos/randomtruth/ / CC BY-NC-SA 2.0

which sends out protoplasmic veins in all directions in search of its prey: bacteria, fungal spores, and other microbes.

Does math underlie that too?

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*I also love how this video was for his mom. : )

{ 4 comments… read them below or add one }

Amy March 26, 2010 at 9:48 am

When I worked my summer internship at NASA Glenn, I was doing research on combustion in microgravity. Gravity totally messes up the natural behavior of flames and flowfields because of buoyancy. The flames I was looking at would form a spiral, Nike-swoosh-like shape, when friction from the air, not gravity, was the dominating force. The same mathematically-described spiral shapes appeared in all sorts of other places:

– in the ocean on the other side of islands that sit in a current (actually directly related to my work – both my air and the ocean water were examples of von Karman swirling flows)
– growth of bacteria colonies and other microorganisms
– human heartbeat electrical signal patterns

This blew my mind. How it was all related. How the patterns were all the same. How the math permeated everything and made it all make sense.

That’s what this post reminded me of.

visitor x March 26, 2010 at 11:32 am

Great subject. Reminds me of an article published in Science (I think). My english (and overall intelligence and knowledge XD) are awful, but I’ll try to do my best explaining the thing as I understood it:

Some researchers were studying the growth pattern of a mold, they did set up certain ammounts of oats scattered all over the place, then looked at how the mold grew towards those nutrients and stablished paths to not only reach them, but to keep those “feeding spots” connected, so the nutrients could travel through the “mold paths” to the entire organism. Of course that behaviour was explained and predicted by some obscure (to me) mathematical algorythm, which the scientists used to build a computer model to generate optimal patterns of net-growth.
But, even more mind-blowing is that, the mold growth pattern, had striking resemblance to the structure of the railways in Tokyo. I mean, the engineers, to keep population centers connected by train, had been using (without knowing it), the same strategies that the mold uses to keep food sources connected.

I hope I didn’t write some silly mistakes, and I would add a link to the source, but I don’t even remember where I read it in the first place.

Molds, maths explaining behaviour, biomimesis… you’ve got to love it.

Jennifer Frazer March 26, 2010 at 12:06 pm

Cool Amy!

And totally, visitor x! I think you got it pretty well right. The scientists actually rigged the experiment by putting the oat flakes at locations corresponding to Japanese rail hubs, making a little japan-shaped coral around the mold and using light to simulate high terrain (slime molds dislike light). And you’re right, they did make an algorithm that replicated the feat. I actually wrote about that experiment too.

I just wonder if there’s some more fundamental math that can explain why an oak tree, with a very different mechanism (presumably) for deciding which branches go where, can, when expressed as a 2-D image, look so similar to the slime’s feeding pattern.

visitor x March 26, 2010 at 5:31 pm

Wow, I got pretty close!. I should’ve known that you knew (and wrote) about it, this really is a great blog.

And about oaks, slimes ┬┐and trains?… this is a midnight (Spanish time) rambling, but I’m thinking it must be evolutive convergence, but, what guides that convergence? maybe the mechanisms and objectives of those beings are, in a very basic level, more similar than we think, and given the tools they have, (ramifications, conduits, trial and error…) maybe there’s one single most efficient way for them to accomplish their goals. That “way” has to be able to be expressed by maths, and maybe that “formula” is some kind of ideal configuration to which those organisms tend: if one of them goes the opposite way, it would be “punished” by natural selecction, and it would be “rewarded” otherwise… you know the drill.
The moral of my rambling being: I bet that there’s some fundamental phenomena at the core of it, and it would explain all these similarities, and I double-bet that maths will be able to determine it. 8^)

And I triple-bet that this is the right time for me to get some sleep!. Bye and thanks!.

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