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单词 fractal
释义

fractaln.adj.

Brit. /ˈfraktl/, U.S. /ˈfrækt(ə)l/
Etymology: < French fractal (B. B. Mandelbrot 1975, in Les Objets Fractals), < Latin fractus , past participle of frangĕre to break: see -al suffix1.
Mathematics.
A mathematically conceived curve such that any small part of it, enlarged, has the same statistical character as the original. Frequently attributive or as adj.
ΘΚΠ
the world > relative properties > number > geometry > curve > [noun] > other
quadratrix1656
section1665
family1705
semiparabola1728
tractrix1728
witcha1760
tractory1820
sinusoid1823
tractatrix1828
indicatrix1841
hodograph1847
tetrazomal1867
space curve1875
horograph1879
hypercycle1889
Peano curve1900
multiple arc1967
unknot1971
fractal1975
analemma1978
the world > relative properties > number > geometry > curve > [adjective] > having certain property
mechanical1694
intercepted1702
rectifiable1706
transcendental1706
tortuous1867
monocyclic1869
bicursal1873
irreconcilable1881
closed1882
anautotomic1901
fractal1975
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 good deal more 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 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.
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 Sci. Amer. Apr. 21/2 Among the fractals that exhibit strong regularity the best-known are the Peano curves that completely fill the finite region and the beautiful snowflake curve discovered by the Swedish mathematician Helge von Koch in 1904.
1984 Nature 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.
1985 Nature 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.
This entry has not yet been fully updated (first published 1989; most recently modified version published online March 2022).
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n.adj.1975
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