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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 De Rham curve ： ウィキペディア英語版 De Rham curve In mathematics, a de Rham curve is a certain type of fractal curve named in honor of Georges de Rham. The Cantor function, Cesàro curve, Minkowski's question mark function, the Lévy C curve, the blancmange curve and the Koch curve are all special cases of the general de Rham curve. ==Construction== Consider some metric space $(M,d)$ (generally $\backslash mathbb$2 with the usual euclidean distance), and a pair of contracting maps on M: :$d\_0:\backslash \; M\; \backslash to\; M$ :$d\_1:\backslash \; M\; \backslash to\; M.$ By the Banach fixed point theorem, these have fixed points $p\_0$ and $p\_1$ respectively. Let ''x'' be a real number in the interval $()$, having binary expansion :$x\; =\; \backslash sum\_^\backslash infty\; \backslash frac,$ where each $b\_k$ is 0 or 1. Consider the map :$c\_x:\backslash \; M\; \backslash to\; M$ defined by :$c\_x\; =\; d\_\; \backslash circ\; d\_\; \backslash circ\; \backslash cdots\; \backslash circ\; d\_\; \backslash circ\; \backslash cdots,$ where $\backslash circ$ denotes function composition. It can be shown that each $c\_x$ will map the common basin of attraction of $d\_0$ and $d\_1$ to a single point $p\_x$ in $M$. The collection of points $p\_x$, parameterized by a single real parameter ''x'', is known as the de Rham curve. 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「De Rham curve」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.