
16 Friction-Induced Vibration and Self-Organization
and surfaces, including their non-integer dimensions, were studied by
mathematicians in the 1930s. The word fractal was coined in 1975 by Benoit
Mandelbrot, who popularized the concept of self-similarity and showed
that fractal geometry is universal in nature and in engineering applications
(Mandelbrot 1982). The fractal concepts were applied to rough surfaces. In
the late 1980s through the early 1990s, the fractal geometry approach was
introduced into the study of engineering rough surfaces by Gagnepain and
Roques-Carnes (1986), Ling (1989), Majumdar and Bhushan (1990), and others
(Nosono