Scientists still puzzled by a fractal discovered 500 years ago

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In between painting the Mona Lisa and idly designing flying machines for fun, Leonardo Da Vinci occasionally got outside and looked up every now and again. Because he was Da Vinci, the moment he did, he discovered a new natural law. This one was about trees, and after five hundred years, scientists are still trying to figure out why the law worked in the first place.

Strip the leaves off of the average tree, soak the whole thing in water until it gets mushy, bundle the branches up together, and you'll get what looks like one long trunk. That's what Leonardo Da Vinci said in the fifteen hundreds. If a tree trunk splits off into three main branches, each of the branches will be one third the size of the trunk. When each of those branches splits into three again, making nine branches on the second 'tier' of the tree, each of these second tier branches will be one ninth the side of the trunk. As the branches grow and split, they will always be a particular fraction of the size of the trunk, and adding together all the fractional bits of each 'tier' of branches will always add up to 'one trunk.' This isn't the case in all trees, but the majority hold to this pattern.

The reason for this, to me, is obvious: Trees love fractions. They're like third grade teachers that way. (They're also like third grade teachers in that they don't like it when kids play with matches, but that was probably the subject of a separate Da Vinci observation.)


Scientists wanted to come up with a different reason for tree-based-math, and so they've been testing this old observation of Leonardo's. There are two main schools of thought. One holds that this kind of structure allows trees to move sap from the thick, but short, lower trunk to the high branches. The second says that trees need to use this structure to withstand stresses. The second theory got a little evidence to back it up recently, even though it was virtual evidence. Christophe Eloy, of the University of Provence in France, put virtual trees in a virtual wind tunnel. The branches, and trees, that held with Leonardo's Rule of Trees held together longer, and under tougher conditions, than those that branched out in their own way. Still the hydrologists hold firm that their model is also better served by this particular tree pattern.

This pattern of growth has a mathematical, as well as physical, beauty. Trees are natural fractals, patterns that repeat smaller and smaller copies of themselves. Each tree branch, from the trunk to the tips, is a copy of the one that came before it. Branches split off from the highest tip the same way they do from the trunk, and set of branches splits off at the same angle to each other. Physics, math, and biology come together to create the simplest and most efficient growth pattern. It just took Leonardo Da Vinci to first notice it, the big show-off.


Image: Solkoll

Via Physics Central.