Mandelbrot setn.

Brit.

/ˈmandlˌbrəʊt ˌsɛt/,

/ˈmandlˌbrɒt ˌsɛt/, U.S.

/ˈmæn(d)lˌbrɑt ˈˌsɛt/

Origin: From a proper name, combined with an English element. Etymons: proper name Mandelbrot , set n.²

Etymology: < the name of Benoit B. Mandelbrot (1924–2010), Polish-born U.S. mathematician who investigated the concept + set n.²

Mathematics.

The set of all complex numbers c for which the Julia set of the mapping z → z² + c is connected, where z is a complex variable; the set of all complex numbers c such that under repeated application of the mapping z → z² + c any complex number z remains within a bounded region of the complex plane. Also in extended use.When represented graphically on the complex plane, the Mandelbrot set has a distinctive, highly convoluted fractal boundary which can only be drawn accurately by a computer. Its basic shape (to the naked eye) is that of a cardioid with one large and two smaller circular shapes attached symmetrically to the boundary. Each of these shapes has more, smaller shapes attached, and so on, so that no matter how much a portion of the boundary is magnified, further magnification always reveals more detail.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set

set1857

interval1902

intersection1909

union1912

lattice1933

matroid1935

closure1937

Steiner triple or triplet system1939

recursive set1943

convex hull1951

power set1953

convex envelope1964

Steiner system1966

Julia set1976

Mandelbrot set1984

1984 Bull. Amer. Math. Soc. 11 127 Many important open questions regarding quadratics are best phrased in terms of the Mandelbrot set.

1984 Bull. Amer. Math. Soc. 11 129 This computer evidence strongly suggests that the Mandelbrot set is also a fractal and that the dynamics always bifurcates according to the same ‘pattern’.

1985 Sci. Amer. Aug. 8/1 The boundary of the Mandelbrot set is a fractal, but it is also much more.

1986 Nature 16 Oct. 590/2 Peitgen and Richter present high-resolution computer-generated images of the Julia and Mandelbrot sets, vividly coloured to illustrate their important mathematical properties.

1988 Bookseller 23 Sept. 1221 Yuval Fischer introduces the fundamentals of a new, extremely efficient algorithm for the Mandelbrot set.

1989 J. J. McGann Towards Lit. of Knowl. p. x Rather, the move asks the reader to imagine the poetical work as a kind of Mandelbrot set.

1993 R. Rucker et al. Mondo 2000 (U.K. ed.) 10/2 The Mandelbrot set is shaped like big, fat, warty buttocks with a knobby disk stuck on one side, and with a bumpy stinger sticking out of the disk.

1994 J. Barth Once upon Time 180 History is a Mandelbrot Set, infinitely subdivisible.

This entry has been updated (OED Third Edition, September 2000; most recently modified version published online March 2022).

单词	mandelbrot set
释义	Mandelbrot setn. Brit. /ˈmandlˌbrəʊt ˌsɛt/, /ˈmandlˌbrɒt ˌsɛt/, U.S. /ˈmæn(d)lˌbrɑt ˈˌsɛt/ Origin: From a proper name, combined with an English element. Etymons: proper name Mandelbrot , set n.² Etymology: < the name of Benoit B. Mandelbrot (1924–2010), Polish-born U.S. mathematician who investigated the concept + set n.² Mathematics. The set of all complex numbers c for which the Julia set of the mapping z → z² + c is connected, where z is a complex variable; the set of all complex numbers c such that under repeated application of the mapping z → z² + c any complex number z remains within a bounded region of the complex plane. Also in extended use.When represented graphically on the complex plane, the Mandelbrot set has a distinctive, highly convoluted fractal boundary which can only be drawn accurately by a computer. Its basic shape (to the naked eye) is that of a cardioid with one large and two smaller circular shapes attached symmetrically to the boundary. Each of these shapes has more, smaller shapes attached, and so on, so that no matter how much a portion of the boundary is magnified, further magnification always reveals more detail. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set set1857 interval1902 intersection1909 union1912 lattice1933 matroid1935 closure1937 Steiner triple or triplet system1939 recursive set1943 convex hull1951 power set1953 convex envelope1964 Steiner system1966 Julia set1976 Mandelbrot set1984 1984 Bull. Amer. Math. Soc. 11 127 Many important open questions regarding quadratics are best phrased in terms of the Mandelbrot set. 1984 Bull. Amer. Math. Soc. 11 129 This computer evidence strongly suggests that the Mandelbrot set is also a fractal and that the dynamics always bifurcates according to the same ‘pattern’. 1985 Sci. Amer. Aug. 8/1 The boundary of the Mandelbrot set is a fractal, but it is also much more. 1986 Nature 16 Oct. 590/2 Peitgen and Richter present high-resolution computer-generated images of the Julia and Mandelbrot sets, vividly coloured to illustrate their important mathematical properties. 1988 Bookseller 23 Sept. 1221 Yuval Fischer introduces the fundamentals of a new, extremely efficient algorithm for the Mandelbrot set. 1989 J. J. McGann Towards Lit. of Knowl. p. x Rather, the move asks the reader to imagine the poetical work as a kind of Mandelbrot set. 1993 R. Rucker et al. Mondo 2000 (U.K. ed.) 10/2 The Mandelbrot set is shaped like big, fat, warty buttocks with a knobby disk stuck on one side, and with a bumpy stinger sticking out of the disk. 1994 J. Barth Once upon Time 180 History is a Mandelbrot Set, infinitely subdivisible. This entry has been updated (OED Third Edition, September 2000; most recently modified version published online March 2022). < n.1984
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