Fractal Processes

The concept of fractals is often considered to describe surface roughness. Fractals retain all the structural information and are characterized by a single descriptor, the fractal dimension, D. Fractal dimension is an intrinsic property of the surface and independent of the filter processing of measuring instrument as well as the sampling length scale. This book cover fractal analysis of surface roughness in different machining processes such as Computer Numeric Control (CNC) end milling, CNC turning, electrical discharge machining and cylindrical grinding. The content here presented adds a significant contribution to the existing literature, with interest to both industrial and academic public.

Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics, biology, finance, and medicine. Since most convincing models contain an element of randomness, stochastics enters the area in a natural way. This book documents the establishment of fractal geometry as a substantial mathematical theory. As in the previous volumes, which appeared in 1998 and 2000, leading experts known for clear exposition were selected as authors. They survey their field of expertise, emphasizing recent developments and open problems. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.

In Chapter One we review the foundations of statistieal physies and frac­ tal functions.