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单词 fractal
释义 fractal, n. (and a.) Math.|ˈfræktəl|
[a. F. fractal (B. B. Mandelbrot 1975, in Les Objets Fractals), f. L. fract-us, pa. pple. of frangĕre to break: see -al1.]
A mathematically conceived curve such that any small part of it, enlarged, has the same statistical character as the original. Freq. attrib. or as adj.
1975Sci. 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 good deal more can be described by the use of generalized Brownian motions and the idea of the fractal dimension.1977B. B. Mandelbrot Fractals i. 1/2 Many important spatial patterns of Nature are either irregular or fragmented to such an extreme degree that..classical geometry..is hardly of any help in describing their form... I hope to show that it is possible in many cases to remedy this absence of geometric representation by using a family of shapes I propose to call fractals—or fractal sets.1977Sci. 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 snowflake curve s.v. snowflake 7].1984Nature 4 Oct. 419/2 Parts of such patterns, when magnified, are indistinguishable from the whole. The patterns are characterized by a fractal dimension; the value log2 3 ≃ 1·59 is the most common.1985Ibid. 21 Feb. 671 Mandelbrot has argued that a wide range 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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