It has recently come to my attention that the general public is not familiar with fractals. I have mistakenly been believing that fractals are awesome enough to escape the confines of the mathematical world and be beloved by math nerds and non-math people alike.

Fractals are beautiful, which is why I thought they would be well known to the general population. You don't have to understand anything about iterations, rectifiablity, or recursiveness to appreciate them. And you don't have to know who Mandelbrot, Sierpinski, or Lévy were to admire the fractals they developed.

Fractals are images that are created by repeatedly performing a certain "step." That step can be either simple and easy to explain in words, or extremely complicated. But what am I saying, no one wants to know how to make a fractal, and if you do check out the classic, easy-to-understand iterations that make the Koch Snowflake. Or to watch the Mandelbrot Set developing, go to this
Fractal Applet, choose your favorite color scheme (I prefer Purple Haze) and walk through the iterations.

A fractal is a geometrical design in which, roughly speaking, each part looks like the whole. A real life example is broccoli. Take the biggest bunch of broccoli in your fridge, now break off a large floret and a smaller floret off of that one. If you stand them up next to each other, other than differences in size, they should look roughly the same. It's the same in a fractal, you can zoom in anywhere on the curve and not be able to tell how far you've zoomed in.

There's also lots of really fun math you can do with fractals, like trying to determine the perimeter of the Koch Snowflake or volume of the Menger Sponge. Fractals are also good for gazing at and contemplating the unfathomableness of life.