How to Think Like Benjamin Graham and Invest Like Warren Buffett

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FIGURE 3-1 Driven pendulum time series.

force. It will swing bac kand forth at a steady speed and not come
to rest (unless we withdraw its force). A Cartesian time-series plot
would show such a pendulum’s motion as a wavy up-and-down line
whose height remains the same as time passes, as shown in Figure
3-1.^7
The driven pendulum’s portrait in phase space can be envisioned
as a rectangle. At any moment in phase space, the pendulum’s angle
would dictate the location of a point horizontally and the pendulum’s
speed would dictate the location of a point vertically. As such, the
pendulum’s portrait in phase space would form a loop, illustrating
the pendulum’s continual motion through the same sequence of po-
sitions repeatedly, as shown in Figure 3-2. That continual repetition
is described as a limit cycle or a limit cycle attractor because the
pendulum (which can be called a system) is attracted to that one
and only (limit) cycle.
Now consider a pendulum undriven by permanent mechanical
force, having instead been started manually by lifting it to one end
of its orbit and letting it go. Without the permanent mechanical
force, the undriven pendulum will swing bac kand forth, gradually
reducing speed and coming closer and closer to rest. A Cartesian
time-series plot of this undriven pendulum would begin with the
same wavy up-and-down line depicting the driven pendulum just