fractal dimensions

Fractals are shapes that are made up of smaller versions of the same shape. For example, a fractal triangle is made up of smaller triangles all inside of one another. It can keep going on and on. The length of the top line of a fractal triangle will never be the same as the length of the second line, instead the length of the top line will be a fraction of the length of the second line. To measure how much smaller each of the parts inside the shape are, we use a number called the fractal dimension. The fractal dimension tells us how complex the shape is and how many details there are in the shape. As the fractal dimension gets bigger, the shape gets more and more complex.