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• fractal ('frasktel), sb. (and a.) Math. [a. F. fractal (B. B. Mandelbrot 1975, in Les Objets Fractals), f. L. fract-us_y pa. pple. offrangere to break: see -AL¹.] A mathematically conceived curve such that any smali part of it, enlarged, has the same statistical character as the original. Freq. attrib. or as ad).

1975 Sci. Amer. Nov. 144/3 It seems that mountain relief, islands, lakes, the holes in Appenzeller and Ementhaler cheeses, the craters of the moon, the distribution of stars close to us in the galaxy and a go od de al morę can be described by the use of generalized Brownian motions and the idea of the fractal dimension. 1977 B. B. MANDELBROT Fractals i. 1/2 Many important spatial pattems of Naturę are either irregular or fragmented to such an extreme degree that.. clas sic al geometry..is hardly of any help in describing their form... I hope to show that it is possible in many c as es to remedy this absence of geometrie representation by using a family of shapes I propose to cali fractals - or fractal sets. 1977 Sci. News 20 Aug. 123 Sets and curves with the discordant dimensional behavior of fractals were introduced at the end of the 19th century by Georg Cantor and Karl Weierstrass. 1978 [see snowjlake curve s.v. SNOWFLAKE 7], 1984 Naturę 4 Oct. 419/2 Parts of such pattems, when magnified, are indistinguishable from the whole. The pattems are characterized by a fractal dimension; the value log2 3 - 1-59 is the most common. 1985 Ibid. 21 Feb. 671 Mandelbrot has argued that a wide rangę of natural objects and phenomena are fractals; examples of fractal trees include actual trees, plants such as a cauliflower, river systems and the cardiovascular system.

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