What makes chaos theory and fractals interesting (beyond the art) is that they have an interesting phenomenon - a basic equation can have very complex results. And that mimics much of nature.
Anyone studying trees for instance, cannot fail to recognise that, despite every tree being different, every tree within the species follows the same rules for it's 'random' growth.
Another example - a pile of sand. Everyone knows that if you put one grain of sand on top of another, it is likely to fall off. But if you add more grains, eventually a pile starts to form, ie, the grains are not falling off. And then when you have a nice large pile something strange starts to happen. One grain might sit on top, or it might slide completely down the side and end up on the floor. Or, it might start a chain reaction, an avalanche.

Now both of these systems are starting with a fairly simple set of known rules. Trees grow to follow the sun. They bud offshoots with an alarming regularity. Gravity makes things fall. Friction can stop them. Given these rules, why don't all trees of the same species grow identically, or all sand piles avalanche at the same height?

It has been shown that both of these examples can be modelled with fairly simple equations, and such equations are basically what comprise chaos theory. Fractals are used in computer graphics to draw trees, plants, coastlines etc.