Mandelbrot, known as the father of fractal geometry, was a mathematician who was able to combine mathematics, science, art, and nature. His formulas were genius; his fractals were used to describe mountains, coastlines, snow flakes, lightening, blood vessels, clusters of galaxies, and even cauliflower. Fractals have contributed to chaos theory, geology, medicine, cosmology, engineering, and were even featured in novels such as Jurassic Park.
If you would like to make a simple fractal (the kind found in Jurassic Park), simply take a strip of paper and fold it in half (the first iteration). Fold it in half again (the second iteration). Keep folding it in half. If you could keep doing this, you would eventually end up with the dragon fractal (the 16th iteration is pictured above). You can learn much more about this and other fractals at http://math.rice.edu/~lanius/frac/ . The site includes notes for teachers, printable versions, and directions for making a variety of fractals.