A particular fractal, called Menger's Sponge, is all about surface appearances. It's a purely theoretical shape that has infinite surface area and no volume whatsoever. And because of that, it doesn't occupy three dimensions. Or two. It manages to exist in fractional dimensions.

Almost everyone played with wooden building blocks at some point as a child. That activity might have seemed pointless at the time, but it will now help you understand a particular fractal. Isn't childhood development weird?

Think of gluing toy building blocks together to make a large cube. The cube is three by three, meaning that it has twenty-seven blocks in total, and each face has nine blocks each (although some of those blocks show up on multiple faces, of course). Now take the cube, and remove the center block of each face, as well as the center block of the entire cube. What you'll have left is a hollow set of 'lines,' each made up of three blocks, defining the edges of the cube.

Now look closer. Imagine that each of those three blocks, which define each edge of the cube, is made of smaller building blocks. These blocks are miniature versions of the original cube, with smaller building blocks all glued together, three by three. Do the same thing to each of these mini-cubes that you did to the larger one. Remove the center block of each face and the center block of the cube. Now each of the blocks that make up the original hollow cube is also made up of a hollow cube, and the surface will begin to look pitted.