Eye-Catching Math is a series about beautiful mathematical images. Read more about it here.

A fractal is a pattern that contains smaller and smaller versions of itself. In a fractal, those smaller versions contain even smaller versions of the whole pattern. Theoretically, these smaller versions continue on forever, although when we draw them, we have to stop at some point.

Here is an example of a fractal, called a Koch curve. To make this, draw a particular pointy line, _/\_. Then, replace each edge of _/\_ with a mini version of _/\_. Do that again with each of the new, smaller edges. And so on.

 

When we zoom in on this fractal, we see that it is made up of smaller and smaller versions of itself.

 

Fractals are a wonderful source of artistic inspiration.

 

Fractals are the key idea behind self-similar pictures like this one.

 

Fractal patterns are found in nature surprisingly often.

In trees and clouds:

Dandelions:

Peacock tails:

Even broccoli:

 

Questions about fractals? Feel free to ask in the comments.

More Eye-Catching Math posts coming soon! They will be interspersed with regular blog content.