Handbook of Psychology, Volume 5, Personality and Social Psychology

200 Self-Regulatory Perspectives on Personality

the system into proximity to them. Each attractor has a basin,
which is the attractor’s region of attraction. Trajectories that
enter the basin tend to move toward that attractor (Brown,
1995).
There are several kinds of attractors, some very simple,
others more complex. In a point attractor, all trajectories con-
verge onto some point in phase space, no matter where they
begin (e.g., body temperature). Of greater interest are chaotic
attractors. The pattern to which this term refers is an irregular
and unpredictable movement around two or more attraction
points. An example is the Lorenz attractor (Figure 8.7),
named for the man who first plotted it (Lorenz, 1963). It has
two attraction zones. Plotting the behavior of this system
over time yields a tendency to loop around both attractors,
but to do so unpredictably. Shifts from one basin to the other
seem random.
The behavior of this system displays sensitivity to initial
conditions. A small change in starting point changes the spe-
cific path of motion entirely. The general tendencies remain
the same—that is, the revolving around both attractors. But
details such as the number of revolutions around one before
deflection to the other form an entirely different pattern. The
trajectory over many iterations shows this same sensitivity to
small differences. As the system continues, it often nearly re-
peats itself but never quite does, and what seem nearly iden-
tical paths sometimes diverge abruptly, with one path leading
to one attractor and the adjacent path leading to the other.
A phase space also contains regions called repellers, re-
gions that are hardly ever occupied. Indeed, these regions
seem to be actively avoided. That is, wandering into the basin

of a repeller leads to a rapid escape from that region of phase

space.

Another Way of Picturing Attractors

The phase-space diagram gives a vivid visual sense of what

an attractor looks and acts like. Another common depiction

of attractors is shown in Figure 8.8. In this view, attractor

basins are basins or valleys in a surface (more technically

called local minima). Repellers are ridges. This view assumes

a metaphoric “gravitational” drift downward in the diagram,

but other forces are presumed to be operative in all directions.

For simplicity, this portrayal usually is done in two dimen-

sions (sometimes 3), but keep in mind that the diagram often

assumes the merging of a large number of dimensions into

the horizontal axis.

The behavior of the system at a given moment is repre-

sented as a ball on the surface. If the ball is in a valley (points

Figure 8.7 The Lorenz attractor, an example of what is known as a chaotic
attractor or strange attractor. Source:From C. S. Carver and M. F. Scheier,
On the Self-Regulation of Behavior, copyright 1998, Cambridge University
Press. Reprinted with permission.

Figure 8.8 Another way to portray attractors. Panel A: Attractor basins as

valleys in a surface (local minima). Behavior of the system is represented as

a ball. If the ball is in a valley (point 1 or 2), it is in an attractor basin and will

tend to stay there unless disturbed. If the ball is on a ridge (between 1 and 2),

it will tend to escape its current location and move to an attractor. Panel B: A

wider basin (1) attracts more trajectories than a narrower basin (2). A steeply

sloping basin (2) attracts more abruptlyany trajectory that enters the basin

than does a more gradually sloping basin (1). Panel C: A system in which

attractor 1 is very stable, and the others are less stable. It will take more

energy to free the ball from attractor 1 than from the others. Panel D: The

system’s behavior is energized, much as the shaking of a metaphoric tam-

bourine surface, keeping the system’s behavior in flux and less than com-

pletely captured by any particular attractor. Still, more shaking will be

required to escape from attractor 1 than attractor 2. Source:From C. S.

Carver and M. F. Scheier,On the Self-Regulation of Behavior, copyright

1998, Cambridge University Press. Reprinted with permission.

(A)

1

1

1

1

2

2

2

2

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(B)

(C)

(D)