In this book graphic images are generated using the software Mathematica. The programmes used for generating these graphics are easily adaptable to many variations. These graphic images are enhanced by introducing a variety of different coloring techniques. Detailed instructions are given for the construction of some interesting 2D and 3D fractals using iterated function systems as well as the construction of many different types of Julia sets and parameter sets such as the Mandelbrot set." The beginning Mathematica user will find this a very interesting way to learn the basic commands and programming techniques of Mathematica, such as pure functions, the use of tables etc., since the results of their efforts will be exciting graphic images.