Introducing Chaos: A Graphic Guide (Graphic Guides)

by Iwona Abrams

Ancient Chinese thought recognized that chaos and order are related. In Chinese myth, the dragon represents the principle of order, yang, which emerges from chaos. In some Chinese creation stories, a ray of pure light, yin, emerges out of chaos and builds the sky. Yin and yang, the female and male principles, act to create the universe. But even after they have emerged from chaos, yin and yang still retain the qualities of chaos. Too much of either brings back chaos.

Chaos is a dynamic phenomenon. It occurs when something changes.

chaos is the occurrence of aperiodic, apparently random events in a deterministic system. In chaos there is order, and in order there lies chaos. The two are more closely connected than we ever thought before.

Feedback is a characteristic of any system in which the output, or result, affects the input of the system, thus altering its operation.

The reason why the three-body problem cannot be solved is that gravity is a nonlinear force (specifically, it is “inverse square”), and in a three-body system each body exerts its force on the other two. This produces nonlinear feedback and results in chaotic motion of the moons’ orbits. But we have now “solved” the three-body problem by demonstrating that the orbits are inherently unpredictable.

A distinguishing feature of systems studied by chaos theory is that unstable aperiodic behaviour can be found in mathematically simple systems. Very simple, rigorously defined mathematical models can display behaviour that is awesomely complex. Another distinguishing characteristic of chaotic systems is their sensitive dependence on initial conditions – infinitesimally small changes at the start lead to bigger changes later. This behaviour is described as the signature of chaos.

“It implies that two states differing by imperceptible amounts may eventually evolve into two considerably different states. If, then, there is any error whatever in observing the present state – and in any real system such errors seem inevitable – an acceptable prediction of the instantaneous state in the distant future may well be impossible.”