<table><tr><td width=200 valign=top> <p> <img src=../../home/home_page/home.jpg width=170 height=240> <br>Robert John Morton <p>About my interest in: <h3>Chaos Theory</h3> <p> <a href=../intro/intro_frame.htm>Introduction</a><br> <a href=../difeqn/difeqn_frame.htm>Difference Equation</a><br> <a href=../bifmap/bifmap_frame.htm>Bifurcation Maps</a><br> <a href=../mandel/mandel_frame.htm>Mandelbrot Set</a><br> <a href=../henon/henon_frame.htm>H&eacute;non's Attractor</a><br> <a href=../feig/feig_frame.htm>Iterative Function</a><br> <a href=../lissajou/lissajou_frame.htm>Lissajou's Figures</a> <p><a href=../../index.htm>Home Page/Email</a> <p><a href=../intro/intro_br_frame.htm> <img src=../../images/brazil.gif width=48 height=31 border=0></a> <br>Clique na bandeira<br>para ler em Português. <td> <h2 align=center>Web Site of Robert John Morton</h2> <h3>Chaos Theory: <big>Introduction</big></h3> <blockquote><p align=justify><i> The rules, by which the elements of nature interact, are simple. Yet the result, when seen on a large scale, appears chaotic. But it is not. It is merely complex. It is also benign. So perhaps, if every individual human relationship were governed by similar rules then a benign egalitarian society should be possible. </i> [<a href=intro_br_frame.htm target=_top>Português</a>] [<a href=../../articles-pdf/chaos_theory_summary_introduction.pdf target=_blank>PDF</a>] </p></blockquote> <h3>Formative Interest</h3> <p align=justify> Even from my A-level days at school, I loved maths. But this affection always suffered an undertow. This was because maths, as I knew it, only ever seemed to deal with what I saw as special cases. It could find the area of a square, a circle and even areas beneath regular curves. But all these are only a few special cases of the irregular shapes that make up the real world. Later I felt disappointed that so-called 'solvable' differential equations only related to a few very special cases of motion like that of a pendulum or electronic oscillator. They could not deal with the unlimited variety of motion we see every day. Chaos Theory was thus a happy revelation. <br><br><h3>Playing With Chaos</h3> <p align=justify> Lorenz's strange attractor showed that even the nastiest of differential equations had solutions. We previously didn't have the eyes to see them. I thus became intrigued by the effect of iterating simple difference equations. Consequently, along with probably thousands of others, I could not resist writing programs to explore these effects for various such equations. This in turn led me to experiment with further programs to display these equations' bifurcation maps. And of course I could not miss out the infamous Mandelbrot Set and H&eacute;non's Strange Attractor. <br><br><h3>Practical Lessons</h3> <p align=justify> Will technology and mass-media marketing eventually drive the global economy into chaos? After all, almost every national economy even now exhibits boom/bust periodicity of increasing violence. Bearing in mind that this behaviour is rooted in nothing more than a fundamental property of numbers, what can politicians - or anybody else for that matter - do to stop it reaching the point of self-destruction? <p align=justify> One could wind technology back 100 years. But it would be unsafe to do that unilaterally. I think a better way may be to study chaos to find out how a technologically advancing tightly-coupled global economy could be made to follow a <em>benign</em> strange attractor. This would be one within the bounds of which no individual could ever suffer violence, humiliation, deprivation, or poverty. <p align=justify> The complex behaviour of the <a href=../../book/chap11/society/society_frame_chaotic.htm>world's weather</a> is determined by the simple rules of engagement which exist between the atoms and molecules of the atmosphere, like zillions of little <a href=../../software/programs/robos/mfms_frame.htm>finite-state machines</a> continually exchanging messages. The complex behaviour of society is determined by the rules of social and economic exchange, which exist between all the individuals that make up society. If the fractal rules that govern these individual relationships were properly engineered, and followed, then the whole world could be a better place. However, doing this would require politicians to change their view of what they govern. They would have to replace their absolute holistic views of 'world', 'nation' and 'corporation', with a relativistic <a href=../../projects/landshare/model/model/model_frame.htm> fractal view</a> in which <em>every</em> individual on this planet is wholly included and seen as equally precious. <hr> &copy; March 1999 Robert John Morton | <a href=../../index.htm>HOME</a> | <a href=../difeqn/difeqn_frame.htm>NEXT</a> </table>