# The Center of Math Blog

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## Thursday, December 18, 2014

### Throwback Fact of the Week - Fractals - 12/18/14

Simply put, fractals are a never-ending pattern. Fractals are often complex patterns that are self-similar (look the same) at any scale. Essentially, when you zoom in or out on a fractal image, you expect to see the same pattern or at the least a very similar one.

This may not sound like a precise definition; that's because it's not. A formal definition of fractals has not been settled upon. However, the man who coined the term fractal, BenoĆ®t Mandelbrot, once described them as, "beautiful, damn hard, increasingly useful. That's fractals."

The math behind these incredibly beautiful objects is outside the scope of this blog post (particularly fractals involving the complex plane). So we will end by simply marveling at a couple of these fractals, to help get a better conceptual idea.
 Koch Snowflake: formed by taking a equilateral triangle and replacing the middle third of each line segment with a pair of equal line segments that form the next "triangle"

Image credit: Maksim. From left to right: Mandelbrot set normal zoom, same set at x6 zoom, and same set at x100 zoom.