单词 | fractal |
释义 | fractaln.adj. 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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