Tl;dr:

Fractals are things that contain near-duplicates of themselves. They're breathtaking, carry some intriguing properties, and are literally everywhere.

Think of a cloud.

What’s the general shape of it? Whether you imagine it as lumpy or wispy, it probably has a general shape, with layers of added details. Start with a big lump, add lumps to that lump, add lumps to those lumps, and smaller lumps on those lumps until you get a cloud-like texture. Well, that’s a fractal. Each of those smaller lumps is pretty much the same as the bigger lump, and they add together to make a complete cloud!

Another quick example:

a tree. Start with one branch (the trunk) and add two branches to it. Now add two branches to the ends of those, and two branches to each of those, and on and on. Suddenly you've got yourself a tree! Do you notice how each branch is pretty much the same as all the others?

Self-similarity.

The idea that a fractal is similar to its parts is partly why fractals are so mind-blowing. With a high-quality fractal you could zoom in on it for days and it would always look pretty much the same! And yet each piece is a unique and distinct part of the whole. But why does nature use them? And what possible use could they be to us?

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