Fractal

Abstract

The term fractal was first coined by the Polish-born, French-American mathe- matician Benoît Mandelbrot in the mid 1970s (cf. at least Mandelbrot 1975; Stewart 2010). It comes from the Latin word fractus “which has the same root of fraction and fragment and means “irregular or fragmented” (cf. Mandelbrot 1982: 3, in Emmer 2012: 7). Furthermore “it is related to frangere which means to break" (cf. Mandel- brot 1982: 4, in Emmer 2012: 7). Loosely speaking, a fractal is a mathematical object, such as a curve, or, more generally, as a set, “that displays exact or approx- imate self-similarity on different scales” (cf. at least Birken and Coon 2008: 134). Put in more technical terms, a fractal is a geometrical set characterized by the so-called property of internal homothety (cf. Mandelbrot 1975; Vialar 2009). It is a version of a Euclidean concept known precisely as homothety (cf. at least Dodge 2012; La Mantia 2004). As it is well known, homotheties are applications of the plane R2 or of the space R3 onto itself.