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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 Hilbert curve ： ウィキペディア英語版 Hilbert curve A Hilbert curve (also known as a Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891,〔D. Hilbert: (Über die stetige Abbildung einer Linie auf ein Flächenstück. ) Mathematische Annalen 38 (1891), 459–460.〕 as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890.〔G.Peano: (Sur une courbe, qui remplit toute une aire plane. ) Mathematische Annalen 36 (1890), 157–160.〕 Because it is space-filling, its Hausdorff dimension is $2$ (precisely, its image is the unit square, whose dimension is 2 in any definition of dimension; its graph is a compact set homeomorphic to the closed unit interval, with Hausdorff dimension 2). $H\_n$ is the $n$th approximation to the limiting curve. The Euclidean length of $H\_n$ is $\backslash textstyle\; 2^n\; -$, i.e., it grows exponentially with $n$, while at the same time always being bounded by a square with a finite area. ==Images== Image:Hilbert_curve_1.svg|Hilbert curve, first order Image:Hilbert_curve_2.svg|Hilbert curves, first and second orders Image:Hilbert_curve_3.svg|Hilbert curves, first to third orders File:HilbertCurveString.JPG|String art Image:Hilbert.png|Hilbert curve, construction color-coded Image:Hilbert512.gif|A Hilbert curve in three dimensions Image:Hilbert3d-step3.png|A 3-D Hilbert curve with color showing progression Image:Hilbert Curve Animation.gif|This GIF file displays an animation of circles traveling along the path of a Hilbert Space filling 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「Hilbert 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.