||Experimental mathematics will likely never be accepted as "real" mathematics by most mathematicians. But for many enthusiasts it has become more than an engaging hobby - it is rather a passion. While such experiments will continue to enhance our mathematical intuition in th futrue, they might also develop into a sophisticated art form.
When, in the spring of 1983, we made our first discoveries about Julia Sets in a computer graphics lab, we were quite ignorant about the mathematical beauty and the depth of the subject. Since that time we have become addicted, and our addiction has led us into a beautiful area of mathematics.
The goal of this exposition is to give a flavor of the subject of Julia Sets which we trac back to a problem posed by Arthur Cayley in 1879. Our computer graphics not only illustrated the beauty that can be found in Julia sets, but they also provided us with insight that led us to some new results. Int this exposition we can give only a short introduction; in fact, this is an excerpt from a longer article entitled "Newton's Method and Julia Sets" which contains more of the background mathematics.