翻訳と辞書 Words near each other ・ Self-schema ・ Self-sealing fuel tank ・ Self-selection bias ・ Self-separation ・ Self-service ・ Self-service laundry ・ Self-service password reset ・ Self-Service Semantic Suite ・ Self-service software ・ Self-service software vendors ・ Self-serving bias ・ Self-shadowing ・ Self-shrinking generator ・ Self-signed certificate ・ Self-similar process ・ Self-similarity ・ Self-similarity matrix ・ Self-Similarity of Network Data Analysis ・ Self-siphoning beads ・ Self-stabilization ・ Self-steering gear ・ Self-stereotyping ・ Self-storage box ・ Self-Strengthening Movement ・ Self-styled orders ・ Self-sufficiency ・ Self-Sufficiency Project ・ Self-surgery ・ Self-sustainability ・ Self-synchronizing code Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Self-similarity ： ウィキペディア英語版 Self-similarity __NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. ==Definition== A compact topological space ''X'' is self-similar if there exists a finite set ''S'' indexing a set of non-surjective homeomorphisms $\backslash$ for which :$X=\backslash bigcup\_\; f\_s(X)$ If $X\backslash subset\; Y$, we call ''X'' self-similar if it is the only non-empty subset of ''Y'' such that the equation above holds for $\backslash$. We call :$\backslash mathfrak=(X,S,\backslash \; )$ a ''self-similar structure''. The homeomorphisms may be iterated, resulting in an iterated function system. The composition of functions creates the algebraic structure of a monoid. When the set ''S'' has only two elements, the monoid is known as the dyadic monoid. The dyadic monoid can be visualized as an infinite binary tree; more generally, if the set ''S'' has ''p'' elements, then the monoid may be represented as a p-adic tree. The automorphisms of the dyadic monoid is the modular group; the automorphisms can be pictured as hyperbolic rotations of the binary tree. A more general notion than self-similarity is Self-affinity. 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「Self-similarity」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.