ABSTRACT
Chaos is quite vulnerable to numerical error, which is controlled by the precision of the computer. This amounts to introducing random noise in the tenth digit, for example, in an algebraic process with infinite precision. The operation of ‘elongation’ followed by ‘folding’ is the most fundamental property of a map generating chaos. Chaos is generated not only by a one-dimensional map but also by more complicated maps or a system of differential equations. It should be noted that chaos is observed in real world phenomena. The existence of chaos in reality makes it not only a subject of mathematics or computational physics but also a subject of experiments or observations in many fields. One-dimensional maps, being so simple, seem to have nothing to do with existing chaos in the real world. Although chaos is a unique phenomenon as yet, it will become a standard subject, such as a regular oscillation, and its position in nature will be properly appreciated.
