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predict how the fluid will flow upon it. If we start with a simple bowl, a parabolic
basin, then the attractor itself is a point at the bowl’s very bottom. Changing the
value of some influential parameter may induce the sudden formation of a small hill,
growing at the center of the basin’s bottom. Now fluid flow in the attractor bowl runs
down to a path around the hill at its bottom. The autonomous motion of the fluid
flows takes place now in a circular orbit. The basin of the new attractor is the
original bowl minus the point at the top of the central hill. The fluid flow around the
hill at the bottom of the basin is circular and is called a limit cycle. Note that the
direction of the rotation of the limit cycle can circle in one direction or the other. |n
some computational simulations, motion alternates between directions. This
suggests the aspect of the born again amphetamine religions, splitting. There is an
unstable and intermixed probability of right versus left turning directions and their
alternation. This vulnerability to directional splitting and often unpredictable
alterations in action themes can represent what seem to be _ paradoxical
combinations of both good and evil in the same strongly faithful, for example, the
apparent bidirectional morality of generous and loving, pederast priests.
These mathematically flavored images of the sudden emergence of a limit
cycle in complex systems was made biologically concrete to me by research
conducted by one of my first graduate students, David Segal. He is now a professor
of psychiatry at the University of California in San Diego. His program of work
involved the administration of very gradually increasing doses of amphetamine to
rats while their behavior was being monitored and recorded by a continuously
running video camera. He documented the behavior of rats in a walled rectangular
space within which, without drugs, they first wandered about randomly and then
settled down to rest in an individually selected, favorite home corner. Segal called
all of these phenomena, patterns of exploratory behavior. At doses of amphetamine
below 2.5 milligrams (mg) per kilogram weight (kg), the exploration of the entire
bounded space proceeded faster than was the case with their salt-water treated
controls, their paths being more uniformly distributed throughout the box. They
spent less time resting in their home corner. At almost precisely 2.5 mg/kg, the rat’s
behavior changed dramatically into an entirely new pattern of continuous circling. As
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