Chaos Introduction

               Chaos theory is among the youngest of the sciences, and has rocketed from its obscure roots in the seventies to become one of the most fascinating fields in existence. At the forefront of much research on physical systems, and already being implemented in fields covering as diverse matter as arrhythmic pacemakers, image compression, and fluid dynamics, chaos science promises to continue to yield absorbing scientific information which may shape the face of science in the future.
Formally, chaos theory is defined as the study of complex nonlinear dynamic systems. Complex
implies just that, nonlinear implies recursion and higher mathematical algorithms, and dynamic
implies nonconstant and nonperiodic. Thus chaos theory is, very generally, the study of forever
changing complex systems based on mathematical concepts of recursion, whether in the form of a
recursive process or a set of differential equations modeling a physical system.

             The most commonly held misconception about chaos theory is that chaos theory is about disorder.Nothing could be further from the truth! Chaos theory is not about disorder! It does not disprove determinism or dictate that ordered systems are impossible; it does not invalidate experimental evidence or claim that modelling complex systems is useless. The "chaos" in chaos theory is order--not simply order, but the very ESSENCE of order.

         It is true that chaos theory dictates that minor changes can cause huge fluctuations. But one of the central concepts of chaos theory is that while it is impossible to exactly predict the state of a system, it is generally quite possible, even easy, to model the overall behavior of a system. Thus, chaos theory lays emphasis not on the disorder of the system--the inherent unpredictability of a
system--but on the order inherent in the system--the universal behavior of similar Chaos theory predicts that complex nonlinear systems are inherently unpredictable--but, at the same time, chaos theory also insures that often, the way to express such an unpredictable system lies not in exact equations, but in representations of the behavior of a system--in plots of strange attractors
or in fractals. Thus, chaos theory, which many think is about unpredictability, is at the same time
about predictability in even the most unstable systems.

        Chaos theory techniques have been used to model biological systems, which are of course some of the most chaotic systems imaginable. Systems of dynamic equations have been used to model everything from population growth to epidemics to arrhythmic heart palpitations.

        In fact, almost any chaotic system can be readily modeled--the stock market provides trends which can be analyzed with strange attractors more readily than with conventional explicit equations; a dripping faucet seems random to the untrained ear, but when plotted as a strange attractor, reveals
an eerie order unexpected by conventional means.