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

Well they can’t see em everywhere, they’re probably mistaking that for the fibonacci sequence and other ratio based stuff. If they were seeing fractals everywhere, they’d be seeing stuff like a strawberry with tiny little exact strawberries for seeds, which also have tiny strawberries for seeds, etc etc.

Fractals are a recursive thing you can get into with math; after repeating a problem, you get a pattern. If that pattern is drawn, like by a computer, it’ll be an infinitely zoomable image thing.

Now, the fibonacci sequence? That’s something to look up.

Start by reading The Golden Section: Natures Greatest Secret by Scott Olsen. Its a breakdown of the underlying concept youre asking about. Its really short and very easy to read.

Let’s say you’re trying to measure how long a coast is. The rough estimate would be to find the end points of what you’re trying to measure, and take the distance. Of course, this won’t be accurate, because the shore isn’t quite straight – there are ins and outs. Alright, no problem, we can measure smaller distances.

The problem is, the longer you do that – the smaller the pieces you look at – the more details you’ll catch. You should probably include the cove, but what if the cove has a large rock at the shore where water doesn’t quite reach around? What with smaller rocks? Do you measure their surface? What about the sand that water goes around and into? Molecules?

The closer you look at something – even where you would’ve previously thought you have something smooth, you find that it’s made of more nonsmooth stuff. A fractal is a shape where this goes infinitely – not quite unlike most of real world. One of their most interesting properties is that they do not have a measurable length – like the coast example.

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).

A fractal, by my understanding, is a self repeating pattern. This means that, as you zoom in closer you just get the same image back. So, take tree formation for an example. You zoom in to the trunk and it divides into two smaller trunks, then into two smaller trunks again, and then eventually it’s splitting into branches, then smaller branches, then even smaller branches, etc. All of those structures (the splits) as very very similar to each other, in fact they are just the same pattern repeating over and over. The same thing with our vascular system in our body. [Here](https://youtu.be/b005iHf8Z3g) is a visualization that may help!