40 ATaleofTwoMarkets
FIGURE 3-2 Driven pendulum phase space: ‘‘limit cycle at-
tractor.’’
described, but this line’s height would fall gradually and continu-
ously as the pendulum’s speed declined, as shown in Figure 3-3.
This pendulum’s portrait in phase space also would begin as if
it might form a loop, but owing to its declining speed, the plot would
begin to spiral inward continuously as the pendulum slowed down.
Correspondingly, the plot would converge to the origin, as shown in
Figure 3-4. The origin in this case is described as a point attractor
because the pendulum (or system) is attracted to that one and only
point.
Another way to approach the pictures is to conceive of the phase
space as a sideways view of the Cartesian time-series plot. It is in
effect a collapsed side view of the gyrations of the simple time-series
graph.
Keep that picture in mind as you consider a third type of attrac-
tor, which physicists call the strange attractor. The strange attractor
describes a system whose phase portrait will be neither a loop nor a
spiraling circle but instead will show some orbits that appear to be
random: They do not repeat and are not periodic. They are, however,
limited in range. In other words, the portrait will exist in a finite
space but will admit of an infinite number of solutions in that finite
space.