Strange attractors
Dynamic systems can be thought of possessing ‘attractors’ in their phase
diagrams. In the case of the simple pendulum the attractor is the single point at
the origin that the motion is directed towards. With the double pendulum it’s
more complicated, but even here the phase portrait will display some regularity
and be attracted to a set of points in the phase diagram. For systems like this the
set of points may form a fractal (see page 100) which is called a ‘strange’
attractor that will have a definite mathematical structure. So all is not lost. In the
new chaos theory, it is not so much ‘chaotic’ chaos that results as ‘regular’ chaos.