The term “fractal” suggests fracturing or splitting. Mathematicians use the term to describe a figure made up of an infinite number of parts, each part a scaled version of a single part, with the scaling constantly diminishing the size of repeated parts. Look closely at a fern, or a head of broccoli. These are finite, or partial, versions of fractals: when you look closely at the parts that compose them, the parts are smaller versions of the whole.
A fractal can be created by beginning with a particular figure or shape and then following a set of recursive instructions. That is, an action is performed on the shape such as adding to it, or splitting it, which creates new smaller shapes similar to the original. The instructions are then applied to these new smaller shapes, and the process repeats again and again, ad infinitum. A fractal tree, for instance, can be created by splitting the original “trunk” into two thick branches that are smaller copies of the trunk. These two branches in turn each split in exactly the same manner, and the process repeats again and again as smaller and smaller branches grow on the tree.