Fractals are inherently natural; and nature loves to repeat patterns. This really isn’t a surprise, because everyone knows that there is alot of symmetry [which is a bit different than patterning, yes] in natural objects. It’s like in π where the Golden Ratio [a sort of fractal] can be found everywhere. For years one of my doodling habits has been, unknowingly, an echo of the Golden Ratio. I draw a right triangle and then section it off by drawing a line perpendicular to the hypotenuse from the right angle of the triangle. The result is two more right triangles, which I then do the same thing to. Smaller and smaller and smaller. Another way of describing fractals uses the example of a coastline, if you’re measuring the length of a coastline, the closer you get the longer the coastline becomes. A finite area bounded by an infinite line.
Asymptotes come to mind here as well, and the old saw about a frog jumping halfway to the pond with each jump. He’ll never reach the pond, mathematically speaking, because he only halves the distance remaining with each jump. This is why I can never know anything, despite the fact that I’ve learned so very much in almost 25 years, I’m still only halfway to wherever there is. This might be a very good explanation for why we can’t ever really know God or reach perfection on our own, but I’m way off track at this point.
Branches were the impetus to write this post. So many things branch, and branch the same way, that it gives me the good willies. When I truly realized that there has to be a reason behind the similarity between rivers and tributaries, the branches of a tree, our veins, capillaries and arteries it was one of those minor mindblowing things that only really occur to me when I see something ubiquitous and mundane as if for the first time. The sphere is another reoccuring pattern, from subatomic particles up to planets- rain is spherical, or would be without the work of gravity. This makes me think that size does not matter. Another thought I had the other day, atoms are mostly empty space. The universe is mostly empty space. Science has this idea of dark matter, and they think it must fill the “empty space” of the universe. I wonder if anyone has thought to look in the empty space of atoms.
Chris Coyne has made a mathematical programming language [redundant, I know] that can create beautiful pictures, including some with branches.