ABSTRACT
The fractal character of a system has many implications for its properties. In particular, a fractal set tends to ll the whole space in which it is embedded and has a highly irregular structure, while it possesses a certain degree of self-similarity; that is, when viewed at increasing levels of magni- cation, a fractal set appears to be the union of many ever smaller copies of itself (Figure 1.1). This character is captured by the so-called fractal dimension, DF, of the set and can be regarded as one measure of the complexity of the system and as the degree at which a set lls the Euclidean space in which it is embedded. The compelling reasons for the emerging fractal theory in many scientic elds are based on the hope that complex systems could be explained using a relatively low number of parameters, say, the fractal dimension DF .
