Side note: I tend to find these people very eccentric, I sorta feel like they can see the matrix 🙂 I am absolutely fascinated by this but completely lost 🙂
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It’s a term to describe patterns that repeat in a predictable way possibly infinitely. Trees have trunks that branch off into branches that branch off into branches which branch off into infinitely smaller branches. Coast lines are just a paradox of constantly measuring longer depending on how tight you measure the coastline, coastline length gets longer and longer depending on how close you focus on how detailed the pattern is. But the way the waves lap at the rocks break down in predictable fashion. When you recognize That predictable fashion you are recognizing a fractal, fractals are everything. Things made up of things bonded to things made of…
There are no definitions of a fractal. A fractal *should* have a few characteristics:
– Self-similarity: when you zoom in, you see approximately the same features as when you zoom out, no matter how much you zoom in.
– Detailed structure: no matter how much you zoom in, there are detailed structure.
– Not boring: not boring shapes like straight lines.
There are attempts to make the above list of characteristics into precise definitions, but so far nothing had been widely adopted.
People who say everywhere and everything is fractal probably think that every objects are made out of atoms and even more fine-grained elementary particle, which means it has detailed structure even when you zoom in a lot.
An example of one way to produce realistic object that are like fractal is to make use of Ising model at critical temperature. Ising models are made out of tiny atomic magnets, which can point in either direction, up or down. Usually there are a lot of biased in the directions, because the magnets prefer to point in the same direction, but heat energy shake them up that make it hard to do so. If there are not enough heat, the tiny magnets will form large blocks that all point in the same directions. If there are too much heat, they fail to settle properly. But in between that, there is a critical temperature where in magnets settle in, but the directions they points do not form giant blocks. Instead, as you keep zooming in and zooming in and look at the shapes formed by magnets pointing in the same direction, you keep seeing new complicated features. This is a phase transition.
That idea is a lot more general. The theory of renormalization group explains that how physical processes are like that: if you zoom in and out at different scale, the process follows the same formula except that the parameter changes. This might be a more sophisticated reason why people say that there are fractal everywhere and in everything.
I think people like that just mean “the closer you look, the more you see”. Like, zoom in enough on a smooth-looking surface and you’ll see the roughness of it.
Which is true, until you reach the level where either ~~wavelengths are too short to see anything~~ the stuff you’re looking at is too short for visible wavelengths or, if you aren’t taking “see” literally but just mean detect, well at some point you’re at quantum physics and you really can’t zoom in more than that.
Fractals themselves are a mathematical concept, not literal stuff. But since reality behaves that way (to a point, see above) they like to say it.
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