I'm sure you all know what fractals look like, but a few pretty pictures never hurt anyone:
Isn't that cool? The key thing about fractals is that if you look at just a small part of it, it resembles the whole thing. For instance, the following picture was obtained by zooming in on the upper left tail of the previous one:
One of the original "big ideas" of complex systems is that fractal patterns seem to appear spontaneously in nature and in human society. Let's look at some examples:
Physical Systems: Pop quiz: is this picture a close-up of a rock you could hold in your hand, or wide shot of a giant cliff face?
I don't know what the answer is. Without some point of reference it's very hard to determine the scale because rocks are fractal: small parts of them look like the whole.
Other examples in physical systems include turbulence (small patches of bumpy air look like large patches) and coastlines (think Norway). These two examples in particular inspired Benoit Mandelbrot to give fractals their name and begin their mathematical exploration.
Biological Systems: Here's an example you're probably familiar with:
And one you probably aren't:
The first was a fern, the second was a vegetable called a chou Romanesco, which has to be the coolest vegetable I've ever seen.
In the case of these living systems, there's a simple reason why you see fractals: they are grown from cells following simple rules. The fern, for example, first grows a single stalk with leaves branching out. These leaves follow the same rule and grow their own leaves, and so on.
Of course, the pattern doesn't exist forever. If you zoom in far enough, eventually you see leaves with no branches. This is an important feature of all real-world fractals: there is some minimum scale (e.g. the atomic scale or the cellular scale) at which the fractal pattern breaks down.
Social Systems: Some people like to extend this reasoning to the social realm, arguing that individuals form families, which form communities and corporations, which form cities, nations and so on. You can try to draw parallels between behavior at the nation level or the corporation level to behavior at the human level.
Personally, I'm a little dubious on this argument. My doubts stem partly from my personal observation that humans seem to act morally on an individual scale, but that corporations on the whole behave far worse than individuals. I think there's something fundamentally different about the centralized decision-making process of a human, and the more decentralized process of a corporation. But this is all my personal opinion. Feel free to debate me on it.
Kurt Gödel's Open World
1 day ago in The Curious Wavefunction