Generating Patterns

Non-deterministic patterns

To make the weather example a little more realistic, introduce a third state - cloudy. Unlike the traffic light example, we cannot expect these three weather states to follow each other deterministically, but we might still hope to model the system that generates a weather pattern.

One way to do this is to assume that the state of the model depends only upon the previous states of the model. This is called the Markov assumption and simplifies problems greatly. Obviously, this may be a gross simplification and much important information may be lost because of it.

When considering the weather, the Markov assumption presumes that today's weather can always be predicted solely given knowledge of the weather of the past few days - factors such as wind, air pressure etc. are not considered. In this example, and many others, such assumptions are obviously unrealistic. Nevertheless, since such simplified systems can be subjected to analysis, we often accept the assumption in the knowledge that it may generate information that is not fully accurate.