FRACTAL BASIN BOUNDARIES
Charles François (2004). FRACTAL BASIN BOUNDARIES, International Encyclopedia of Systems and Cybernetics, 2(1): 1323.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1323 ▶ |
| Object type | Discipline oriented, Methodology or model |
Fractal basin boundaries are discontinuous and practically impossible to precisely pin down. They tend to dissolve into a growingly scattered “dust” of points and the transition of the system from one type of equilibrium to another cannot be properly predicted.
However, by observing, for example, the WEIERSTRASS function, it becomes clear that, at any level, thresholds of instability can be defined, at least tentatively, even if no prediction's validity can be taken for unquestionably secure.
The relative positions of the instability thresholds corresponding to various levels must be considered, since it is important in order to emphasize the normal or extreme character of a situation.