I was introduced to the world of fractals and renormalization groups by Bob Smalley in 1981. At that time Bob had transferred from physics to geology at Cornell as a Ph.D. student. He organized a series of seminars and convinced me of the relevance of these techniques to geological and geophysical problems. Although his official Ph.D. research was in observational seismology, Bob completed several renormalization and fractal projects with me. Subsequently, my graduate students Jie Huang and Cheryl Stewart have greatly broadened my views of the world of chaos and dynamical systems. Original research carried out by these students is included throughout this book.

The purpose of this book is to introduce the fundamental principles of fractals, chaos, and aspects of dynamical systems in the context of geological and geophysical problems. My goal is to introduce the fundamental concepts at the lowest level of mathematics that is consistent with the understanding and application of the concepts. It is clearly impossible to discuss all aspects of applications. I have tried to make the applications reasonably comprehensible to non-earth scientists but may not have succeeded in all cases.

After an introduction, the next seven chapters are devoted to fractals. The fundamental concepts of self-similar fractals are introduced in Chapter 2. Applications of self-similar fractals to fragmentation, seismicity and tectonics, ore grades and tonnage, and clustering are given in the next chapters.