What is a Fractal?

When I first got the idea to learn about fractals, my impression, which may be similar to yours, was that it was a very advanced level of study and that I was not ready to start learning it yet. Boy, was I wrong. Fractal geometry, though I'd like to say is very difficult and you have to be as smart as me to understand it, is actually quite simple. It has to do with three major things that my Algebra 2 class already studied this year: a) functions, b) graphing, and c) imaginary numbers. A function, if you don't know, is an equation that uses any two coordinates and gives you new coordinates. An example of a function is: f(x) = 3x - 1 where f(x) is the y coordinate, 3x is the slope (up three units, to the right one unit), and -1 is the starting point. As a class, we have graphed functions such as this. (see graph below.)

Graphs, of course, can tell us many things. They are especially good for making predictions. For instance, a car is moving at a speed of 50 m.p.h. How far will it go in two hours? We can create a graph from this solution and be able to predict the distance traveled by the car maintaining the same speed after five, ten, even 150 hours. Now, there are different functions for different graphs. You wouldn't use the graph for the car problem if you needed to find the time it would take for a ball to hit the ground after being dropped from a 2,000 foot building. Since the ball would not maintain a constant speed, like the car would, the graph would of course, be curved. All this is true when referring to fractals. A fractal is simply a graph of a different type of function. Hopefully, you're not confused yet. If you're ready to get into the thick mathematics, including the third element of fractal geometry, imaginary numbers, then go on to the next page. If you're totally lost, check out some cool fractal pictures for you're viewing pleasure or go to the links page...maybe someone else's page can explain this easier!