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 🙂

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Answer 1

Excentric might be right. It’s hard to comment on this, because we don’t actually know what those people are talking about, but I suspect they are actually the kind of people that have a casual interest in popularized science and math, and they repeat what they heard or read somewhere. The type of people that will tell you that tomatoes are not vegetables because they heard somewhere that they are fruits Or that will swear up and down about the natural beauty of mathematics then get hilariously mad at you when you tell them about Gödel. Or that will tell you that the Fibonacci spiral is the shape of galaxies and plant leaves and snail shells.

Fractals aren’t “everywhere”. They are a mathematical construct, and most things don’t resemble them at all. The thing about fractals is that:

1. They are self similar, meaning that they contain parts that resemble the whole.
2. They contain these structures at arbitrarily small scales.

Obviously you don’t actually get arbitrarily small scales in nature at all. But some things seem to exhibit this self similarity. Certain leaves for example will grow in a way where they split and seem to grow smaller versions of themselves. Trees in general grow in a way where branches will split from the trunk and grow new branches and so forth. But, much like with the snail shells that sort of look like a logarithmic spiral, you can see that these aren’t actually fractals: those new structures aren’t actually the same as the bigger ones (and, again, they obviously don’t repeat at arbitrary sizes).