Fractals are constructs that, when you look closely at them, contain tiny copies of themselves. There are fractals all over nature, and there was a period in the early nineties, around the time of the first Jurassic Park, that fractals and chaos theory were intensely popular. The most popular mathematical fractal, the Mandelbrot set, was featured on t-shirts and posters everywhere, and how quickly your computer could generate one was the Big Nerd equivalent of how quickly your car could go from 0 to 60 MPH.* Note that the audio to the video contains not only a naughty word or two, but extreme geekery in the form of a Jonathan Coulton song. In the world of living creatures, fractals aren't quite as popular. If you met a bear that was a fractal bear, he'd probably look like this:
and that'd just be weird, right? Vegetables are a little different though; at least a few of them are. People talk about onions having layers like that's something interesting, but the broccoli relatives are the ones that you want to watch out for. If you've ever cut up a broccoli or cauliflower, you've probably noticed that the little stalks are much like the larger bits, at least up until a point. The best representation of a fractal that I've seen in nature is broccoli's cousin, the romanesco. The first time you see one, you tend to think "pointy broccoli." That's because it looks like:
Image courtesy of PD Photo.org under a Creative Commons Public Domain license. which, as you can clearly see, is a pointy broccoli, or something that looks suspiciously like a pointy broccoli. *- The "Magic Eye" or random dot 3D autostereograms were also very popular at that time.** **- Ooh, and fiber optic artwork. People loved that stuff.