When you speak to people that understand fractals, they say everywhere and everything is fractals. I have tried to understand fractals but I am completely lost, can someone please explain it like I’m 5?

Question

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 🙂

In: 17

Answer 1

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.