Fractal Surface Model

Abstract

The study of the fractal nature of surfaces appearing in engineering problems is a comparatively young field. It started in the 1980s and 1990s of the last century with phenomenological descriptions of fractal surface properties. While many ideas were presented before, Mandelbrot’s influence on the field, especially of his 1982 book The Fractal Geometry of Nature [162], can hardly be underestimated. This monograph collected many ideas from different fields and for the first time presented to a broad audience the baffling concept of a curve that is everywhere continuous, but nowhere differentiable.