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In mathematics, iterated function systems or IFSs are a method of constructing fractals; the resulting constructions are always self-similar. IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system"). The canonical example is the Sierpiński gasket, also called the Sierpiński triangle. The functions are normally contractive, which means they bring points closer together and make shapes smaller. Hence, the shape of an IFS fractal is made up of several possibly-overlapping smaller copies of itself, each of which is also made up of copies of itself, ad infinitum. This is the source of its self-similar fractal nature. ==Definition== Formally, an iterated function system is a finite set of contraction mappings on a complete metric space.〔Michael Barnsley, "Fractals Everywhere", Academic Press, Inc., 1988.〕 Symbolically, : is an iterated function system if each is a contraction on the complete metric space . 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「iterated function system」の詳細全文を読む スポンサード リンク
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