Three scientists, Jack Wisdom and his two colleagues Shanton Beale and Francois Mignard, from the Massachusetts Institute of Technology, USA, developed a Newton-inspired mathematical model representative of the motion of Hyperion, and embarked on examining its irregular motion using a supercomputer. In order to “see” the results of their experiment, they drew an image that showed the direction of Hyperion and the variation rate of this direction. In order to simplify the results, they commanded the computer to plot the course of each variable against the other, i.e. the direction against the variation rate on a two-dimensional plotter whenever Hyperion gets to a certain point on its orbit. The outcome was similar to a series of superimposed captures: a black spot, representing Hyperion, that leaps over a paper sheet, with each bound representing one orbit. It turned out that upon each regular variation in the direction of Hyperion, the spot would move regularly in a simple pattern. For instance, if the direction varied seasonably in a repeated round, the spot would spring from several loci to return eventually to its starting point. In case of irregular direction changes, the moving spot would mark the sheet leaving a series of random stains.

The team observed that the pattern of spots depended on the energy governing the movement of Hyperion. Certain types of energy prescribed the formation of a simple and predictable pattern of closed curves resembling islands, while other types generated shapeless zones adorned by random stains.

The mathematical equations adopted were the same in both cases but the disturbance would occur upon modification of the energy value, shifting the behavior of the spot from a predictable regular one to a sporadic chaos.

The pattern is not restricted to Hyperion. In fact, scientists have observed that almost every system premised on deterministic laws can generate an unforeseen irregular motion. Chaos, in this sense, is no longer a purposeless erroneous motion but rather a trend that appears random on the surface but underlies a secret internal discipline. An excellent example is the color blending process which encloses a great deal of secret internal uniformity, however random it seems at face value.

Prior to understanding the origin of chaos, it seems imperative to attend to another question: how can scientists predict the behavior of natural systems? They develop a mathematical model consisting of highly complicated technical equations. In principle, these models operate in a simple manner. The equations determine what the model should do after a short period from their instantaneous activity. The equations simulating weather for instance detect the weather in its present condition, then calculate how it would vary one minute later. Some may think that a 1-minute prediction is of no use but they fail to realize that repeating it 60 times can foretell us the weather conditions in an hour. By replaying the process 42 times, we can forecast the weather for an entire day and for an entire year when replayed 563 times. This operation requires an endless thread of boring recurrent mathematical equations, which can be processed easily only by modern computers. With the use of a supercomputer, the prediction of the weather in 10 days would take around one hour, which explains why scientists are incapable of giving forecasts for an entire year. The motion of tides, which relies on the location of the moon and the sun to the earth, can be predicted for centuries, not only for one year, in case of application of these processes.

What is then the reason for this difference and how is chaos generated? This, we will touch on in the upcoming article.