Fractal geometry in engineering metrology

Abstract

Fractal dimensions have primarily reached the general consciousness in the form of generated profiles such as Koch snowflakes and the writings of the mathematician Benoit Mandelbrot (1977). Their importance as a description of natural objects is still much debated and there is no question that enthusiasm for a new idea has led to misuse and superficial use of fractals in many fields. Most of the “serious” publications in physics and engineering have simply been reports that some particular phenomenon can indeed be described by fractal mathematics, with very few attempts to derive quantitative relationships and hardly any cases in which the fractal dimensions are tied in causal ways to the processes involved.