ABSTRACT
Generaly fractal discusses the roughness of the object in which a certain physical quantity is distributed evenly wherever it is found in the embedding space. Therefore, the fractal dimension of the object will still be the same even if the content is diluted to change the density of the content and then distributed throughout the space exactly in the same way. There are situations in which physical quantities are unevenly distributed over the space. Hence, fractal is insufficient to characterize the object of interest having complex and inhomogeneous scaling properties, since different irregular structure may have same fractal dimension. Thus, this chapter narrates the multifractality in which multifractal dimensions provide more information about the space filling (unevenly distributed) properties than the fractal dimension. Moreover, the multifractal formalism in the context of deterministic as well as random (or stochastic) case is developed in this chapter. Further, this chapter discusses two main features, (i) finding the explicit time dependent and scaling properties of the particle size distribution function, when particles are characterized by more than one variable and (ii) the connection between the kinetics of the fragmentation process and the occurrence of multifractality.
