Fractals are fascinating. A fractal is a self-repeating pattern of some sort which appears exactly the same at all magnification levels. Mathematicians are especially interested in fractals and have studied them over a long period of time. Several books have been written on fractals, for instance The Fractal Geometry of Nature and Fractals Everywhere. Looking closely at nature, we see that there are many things which have a self-similar or self-repeating pattern, which makes them fractals.

There is a TED talk about fractals and the speaker has generously made his tool available online here, where you can play with existing fractal iterations or create your own from scratch. I borrowed some of them here.

Fern: This one shows how a fern leaf can develop from a simple shape of four line segments. Notice how the basic shape repeats itself.

Ethiopian Cross: Did our ancient fathers know about fractals?

Algae: In a similar way to the fern, a complicated object arises from a simple shape.

Many other things in nature, such as lightning, broccoli, human lungs, sea shells, peacock, pineapple, crystals, trees, exhibit a fractal. Captivating designs! Enjoy exploring.