Another example is G. Cantor's ternary set, which is the set of points remaining on a line segment when the operation of dividing a line segment into thirds and leaving two small segments at both ends is repeated infinitely. Another simple self-similar figure in a set on a plane is the Koch curve, discovered by H. von Koch in 1906, and its self-similarity is clear when viewed in a diagram. Around 1967, BB Mandelbrot named the self-similar figures mentioned above and related figures with self-similarity as fractals, and taking advantage of the fact that computers can represent such self-similarity with great accuracy, he has published a number of extremely beautiful fractals. *Some of the terminology that mentions "Koch, H. von" is listed below. Source | Heibonsha World Encyclopedia 2nd Edition | Information |
…もう一つの例はG.カントルの三進集合で,線分を3等分し,両端の二つの小線分を残すという操作を無限に行い,元の線分上に最後まで残っている点の集合である。さらに平面上の集合での簡単な自己相似図形はフォン・コッホH.von Kochが1906年に発見したコッホ曲線であって,その自己相似性は図を見れば明らかであろう。 マンデルブローB.B.Mandelbrotは1967年ころに今まで述べたような自己相似図形やそれに関連した自己相似性をもつ図形をフラクタルと名づけ,コンピューターはこのような自己相似性をきわめて精度よく表現しうることを利用して,きわめて美しいフラクタルの数々を発表している。… ※「Koch,H.von」について言及している用語解説の一部を掲載しています。 出典|株式会社平凡社世界大百科事典 第2版について | 情報 |
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