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題 名 | 混沌的捕捉與視覺化--以自行開發軟體重現知名碎形並蒐尋未知奇異吸子=Capturing and Visualizing the Patterns of Chaos--Reproducing Famous Fractals and Searching for Unknown Strange Attractors |
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作 者 | 黃玉坤; | 書刊名 | 技術學刊 |
卷 期 | 15:2 2000.06[民89.06] |
頁 次 | 頁329-337 |
分類號 | 312.49 |
關鍵詞 | 混沌; 碎形; 奇異吸子; 吸子盆地; Lyapunov指數; 碎形維度; Chaos; Fractals; Strange attractors; Basin of attraction; Lyapunov exponent; Fractal dimension; |
語 文 | 中文(Chinese) |
中文摘要 | 本文旨在以自行開發的軟體重現著名的碎形—H.-O Peitgen稱之為Images of Complex Dynamical Systems—如Mandelbrot集合以及Julia集合,並且蒐尋未知的奇異吸子—包括著名的Lorenz Attractor以及Rossler Attracto,所蒐尋的奇異因子限於多維多項式映射與多項式微分方程系統。碎形和奇異吸子皆與非線性動力系統潛在的混沌現象有很密切的關聯,但本文的目的並不在探討深奧的混沌理論,而是試圖將混沌現象所造成碎形的世界視覺化,相信即使不具專業背景的人士對璀燦繽紛的碎形之美奕能深深受感動,同時我們所開發的軟體亦可以作為將來專業學術研究工具的基礎。因為混沌的發現與研究是電腦發明之後才變成可行的,唯有電腦才有辦法處理混沌現象所造成狂亂如麻的資訊。 |
英文摘要 | This study aims to reproduce some popular fractals, such as the Mandelbrot set and the Julia set, which are referred to as images of complex dynamical systems by H.-O.Peitgen etc., and to search automatically enormous unknown strange attractors which should involve the famous Lorenz Attractor and the Rossler Attracto attractor. Here, strange attractors are restricted to a multi-dimensional map or a system of ordinary differential equation both of which are in polynomial form. Fractals and strange attractors are intimately related to chaos, that is, the potential behavior of nonlinear dynamic systems. However, we are not interested in the profound theory but rather attempt to visualize the fractal world of chaos on the screen of our own personal computer. The major result of our work is the program have developed, which, we believe, could be a basis for scientific research into chaos. |
本系統中英文摘要資訊取自各篇刊載內容。