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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 Hutchinson operator ： ウィキペディア英語版 Hutchinson operator In mathematics, in the study of fractals, a Hutchinson operator is the collective action of a set of contractions, called an iterated function system. The iteration of the operator converges to a unique attractor, which is the often self-similar fixed set of the operator. ==Definition== Let $\backslash$ be an iterated function system, or a set of contractions from a compact set $X$ to itself. The operator $H$ is defined over subsets $S\backslash subset\; X$ as :$H(S)\; =\; \backslash bigcup\_^N\; f\_i(S).\backslash ,$ A key question is to describe the attractors $A=H(A)$ of this operator, which are compact sets. One way of generating such a set is to start with an initial compact set $S\_0\backslash subset\; X$ (which can be a single point, called a seed) and iterate $H$ as follows :$S\_\; =\; H(S\_n)\; =\; \backslash bigcup\_^N\; f\_i(S\_n)$ and taking the limit, the iteration converges to the attractor :$A\; =\; \backslash lim\_\; S\_n\; .$ 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「Hutchinson operator」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.