An Introduction to Chaos Theory

An Introduction to Chaos Theory

Abstract

Nature is complex. It features a multitude of systems
which, simple though they may be, are unpredictable in their behaviour, and
seem not to be governed by the established deterministic laws of classical
physics. For many years, scientists ignored such systems claiming that their
unpredictability was a result of the limitations in the accuracy of
measurements, or pure chance. Others even rejected them as unscientific.
However, in the 1970s, a new theory evolved, which, if its supporters are
right, explains the diversity we observe in nature and provides an accurate and
scientific description of the unpredictable phenomena in question. This is
known as “Chaos Theory”, and the purpose of this article is to provide an
introduction to it together with fractals, the elaborate patterns which have
become its emblem.

混沌学导论

摘要

自然界是纷繁复杂的。它以一个复合的系统为其特征，一个可能很简单，但是却无法被预测的系统，而且看上去是一个不大可能被已经建立的经典物理学的决定论所控制的系统。许多年来，科学家们往往会忽略这样的系统，并且往往宣称：这些系统的不可预知性完全是由于我们的测量精度有限引起的，或者纯粹就是偶然的。其他一些观点，甚至认为这些系统就是不科学的。但是，在20世纪70年代，一种新的理论发展起来，该理论解释自然界中我们所观测到的种种不同，同时给出了这些系统一种精确的科学的描述，虽然有待商榷。这就是现在广为人知的“混沌理论”，而本文的目的就是给大家大致介绍该理论，同时还有分形，和能够成为混沌理论象征的一些精密的图案。