# How does the concept of a fractal differ from that of a traditional geometric shape

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How does the concept of a fractal differ from that of a traditional geometric shape

In: Mathematics

A fractal is a shape such that when you zoom in, it looks the same. You could zoom in or out indefinitely and see the same shape.

This does not work for a traditional shape, you can’t keep zooming in on a triangle to find you see another triangle

In geometry, we can make statements about the relationship between the lengths of different sides of a shape. Fractals’ sides are of infinite length, or they have infinitely many sides.

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You know how a _really_ big circle looks like it’s a straight line when you can only see a small piece of it? And the tighter you zoom into it, the flatter it looks until it’s virtually indistinguishable from a straight line?

Now, take a look at [this piece of land](https://www.google.com/maps/@50.2335678,-5.4961855,28521m/data=!3m1!1e3?entry=ttu), at the tip of Cornwall. As you zoom further in, instead of straight lines, you start seeing more and more details along the coast. Cuts and ridges and rocks and stuff. It doesn’t “want” to become that simple straight line you’d get from zooming in on a circle.

Fractals are like the mathematical version of that map: their distinguishing feature is that, no matter how tightly you zoom in, you never reach that “looks like a straight line” phase. There’s always more detail, more structure, more stuff happening. Where a triangle has three points where it’s not nice and smooth, fractals are not nice and smooth _anywhere at all_.

The most famous sort of fractal, and the sort everybody else is talking about, is self-similar fractals. Literally: shapes that are similar to themselves when you zoom in. [This (very trippy) gif](https://upload.wikimedia.org/wikipedia/commons/a/a4/Mandelbrot_sequence_new.gif) shows that self-similarity for the Mandelbrot set, which is perhaps the single most famous fractal.