### Rhythmic Behavior in Systems

Many systems show regular pulses or rhythms of activity. Consider several terms with slightly different shades of meaning.

Periodicity. This is a general term for something happening at regular intervals. It may or may not be caused by activity in a single system.

If astrophysicists saw a flash every week for 4 weeks in a distant galaxy, they might not know if they were witnessing some­thing important, or even whether the flashes came from the same source, only that they were seeing periodic flashes. If further evidence showed that each flash had the same exact spectral composi­tion, the scientists would suspect they were seeing a cyclic phenomenon coming from a single system.

Cycles. This term implies that a single system is producing repetitious events. For example, we have the annual and monthly cycles due to the arrangement of the earth, moon, and sun, and we have the 24-hour cycle due to the rotation of the earth.

Iterative phenomena. This word implies cycles of behavior with small variations that cumulate to produce a change. For example, if a moon orbiting around a planet picked up a small layer of dust each time, by passing through a dust cloud once per orbit, it would gradually build up a layer of dust on its surface. That would be an iterative process.

Anything that accumulates or forms layers indicates an iterative process. In many sciences, cores are taken to trace processes that unfold over a long time.

Tree cores show growth rings, indicating rainfall and other growing conditions for each year. Ice cores show temperature changes (and capture dust and other atmospheric debris) as ice is deposited year by year.

Because layers are built up on a cyclical basis, they can be used to chart changes through time. That is exactly how cores are used in a variety of sciences.

In computing, an example of an iterative process is recursion. A recursive pro­cedure is a contingent loop: a procedure that restarts itself automatically until a condition is met, such as a task being completed.

The TOTE unit is a simple example of a recursive process. First it tests (e.g. looking to see if the nail is sticking up) then performs an operation (like hitting a nail) then tests again. If necessary the program repeats itself until the task is completed. Then the system exits the routine and moves on to the next task.

Iteration is involved in creating and refining new technologies. In October, 2016, Uber teamed up with Budweiser to send a self-driving Otto semi-trailer truck (full of Budweiser) down I-25 in Colorado for 120 miles (with a human driver in the sleeping compartment as backup and a police escort behind).

This was an effort to be first in what promises to be an important growth trend: self-driving trucks. "We are still in the development stages, iterating on the hardware and software," said Lior Ron, the president and co-founder of Uber's Otto unit. ("Uber self-driving truck..." 2016)

In other words, they will test, analyze the results, and repeat...just like a TOTE unit. Uber and Otto may not be the big winners in this niche; Ford, Waymo, and numerous other manufacturers are competing in this race to perfect a new technology.

One interesting iterative process is fractal construction. Fractal growth occurs when construction routines are repeated over and over, resulting in large structures composed of similar units.

This is an economical way to build a large organism, because only one set of instructions is needed. The instructions are executed repeatedly until some "stop" signal is encountered, built into the genome, or due to limited resources.

The earliest life forms on earth, such as stromatolites and sponges and sea ferns, all used fractal construction. Their bodies consisted of multiple copies of very similar building blocks, one attached to the next, eventually creating large structures.

Many trees use fractal construction when they grow. In effect, they apply the rule "grow the stem, then branch into two, then repeat." The repetitions stop when resources are depleted or the tree reaches an optimal size determined by its genetic control system, switching off the growth.

##### Oscillations

Oscillations occur when a system goes back and forth between two states (or two extremes of a measured value). For example, if an air conditioner runs periodically during a hot day, the temperature in the room will oscillate between higher and lower temperatures. The variable is temperature, and the oscillation will be in the range of a few degrees.

As a rule, oscillations occur because two different forces take turns moving the system in opposite directions. Control systems commonly use opponent processes that can push the system in opposite directions.

In a car, the accelerator and brake are opponent processes. A car using its cruise control on an open highway will oscillate gently as the system "pursues" the desired speed, increasing and decreasing speed as needed.

The principle of oscillation: Oscillations occur when opposing forces take turns influencing a system.

Large oscillations sometimes indicate a poorly adjusted system. Builders say not to put a large furnace in a small house, because the heat will be uneven as the room temperature oscillates between hot and cold, depending on whether the furnace is on or off.

This phenomenon of going too far in one direction or the other, in reaction to a disturbance, is called overcorrection. Overcorrection is a common cause of car accidents.

When drivers drift to one side of a road, they may suddenly notice and overcorrect by turning the steering wheel sharply to the other side. This can spin the car or send it into oncoming traffic.

An example of overcorrection in abnormal psychology is the manic-depressive syndrome or bipolar disorder. In this condition, a person oscillates between states of depression and states of intense emotion and activity called mania.

The bipolar syndrome is due to overcorrection in brain circuits using catecholamines, an important category of neurotransmitters. One of the first effective treatments for bipolar disorder was lithium, which reduces the production of catecholamines.

Reducing the production of catechol­amines damps the oscillations of the bipolar disorder. This is like replacing a too-large furnace with a smaller one, to eliminate large fluctuations of temper­ature in a small house.

A classic example of oscillation involves foxes and rabbits. When there are few foxes, rabbits multiply. When rabbits multiply, foxes have plenty to eat, so the foxes multiply.

When the fox population is large enough to kill off most of the rabbits, the foxes starve, and rabbits start to multiply again. Rabbit and fox populations oscillate, slightly out of phase, with first one population peaking then the other.

Following is an idealized graph showing the oscillation. Real population curves are never this smooth because of other factors such as weather, disease, and competition from other species. However, the general pattern is predictable and reliable.

Idealized interaction of fox and rabbit populations [From wiki.scipy.org, public domain]

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