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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tricorn (mathematics) ： ウィキペディア英語版 Tricorn (mathematics) In mathematics, the tricorn, sometimes called the Mandelbar set, is a fractal defined in a similar way to the Mandelbrot set, but using the mapping $z\; \backslash mapsto\; \backslash bar^2\; +\; c$ instead of $z\; \backslash mapsto\; z^2\; +\; c$ used for the Mandelbrot set. It was introduced by W. D. Crowe, R. Hasson, P. J. Rippon, and P. E. D. Strain-Clark.〔http://iopscience.iop.org/article/10.1088/0951-7715/2/4/003/meta;jsessionid=C9B611C5CF44A8CE77C7344996DADD0C.c1〕 John Milnor found tricorn-like sets as a prototypical configuration in the parameter space of real cubic polynomials, and in various other families of rational maps.〔http://projecteuclid.org/euclid.em/1048709112〕 The characteristic three-cornered shape created by this fractal repeats with variations at different scales, showing the same sort of self-similarity as the Mandelbrot set. In addition to smaller tricorns, smaller versions of the Mandelbrot set are also contained within the tricorn fractal. ==Formal definition== The tricorn $T$ is defined by a family of quadratic antiholomorphic polynomials :$f\_c:\backslash mathbb\; C\backslash to\backslash mathbb\; C$ given by :$f\_c:\; z\backslash mapsto\; \backslash bar^2\; +\; c,$ where $c$ is a complex parameter. For each $c$, one looks at the forward orbit :$(0,\; f\_c(0),\; f\_c(f\_c(0)),\; f\_c(f\_c(f\_c(0))),\; \backslash ldots)$ of the critical point $0$ of the antiholomorphic polynomial $p\_c$. In analogy with the Mandelbrot set, the tricorn is defined as the set of all parameters $c$ for which the forward orbit of the critical point is bounded. This is equivalent to saying that the tricorn is the connectedness locus of the family of quadratic antiholomorphic polynomials; i.e. the set of all parameters $c$ for which the Julia set $J(f\_c)$ is connected. The higher degree analogues of the tricorn are known as the multicorns.〔http://www.worldscientific.com/doi/abs/10.1142/S0218127403008259〕 These are the connectedness loci of the family of antiholomorphic polynomials $f\_c:\; z\backslash mapsto\; \backslash bar^d\; +\; c$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tricorn (mathematics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.