Trees are beautiful when they are lush and green in summer or when they flare with red and gold in autumn. What about winter, when the branches are bare? That’s when it’s easiest to see the self-similar structure in the tree’s branching habit. At each juncture where a bud begins a new branch, the angle of the branch is determined by the tree’s genetics and specific influences in the environment. Each tree species has a standard pattern, which is repeated with every bud, so that the shape of the junctures is the same, broadly speaking, in everything from the first heavy branches on the trunk to the newest fine twig. I’ve talked about this before, but I just can’t get enough of the beauty of these elegant patterns.
There are important biological factors behind a tree’s branching habit, but from a mathematical point of view it reveals a fractal pattern, which has the property of being self-similar. A self-similar structure looks roughly the same at every scale from the largest zoomed-out view to the narrowest closeup. There are practical limits in the real world (if you zoom in far enough you get to individual cells and eventually molecules, which aren’t particularly similar to the tree trunk), but within the range that we can call the tree structure the idea holds. If you zoom in on the picture above each branching region looks like the overall structure of the tree.
Fractals are important in nature and mathematics (as I’ve commented before). They are also very beautiful, and reveal the beauty in the structure of everything around us.
Posted in response to the WordPress photo challenge: Structure