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.

Francesco La Mantia (2020). Fractal. In F. Vercellone, S. Tedesco (a cura di), Glossary of Morphology (pp. 209-214). Springer [10.1007/978-3-030-51324-5_45].

Fractal

Francesco La Mantia
2020

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.
Fractal, Internal Homothety, Dimensions, linearity, non-linearity.
978-3-030-51323-8
Francesco La Mantia (2020). Fractal. In F. Vercellone, S. Tedesco (a cura di), Glossary of Morphology (pp. 209-214). Springer [10.1007/978-3-030-51324-5_45].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/479794
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