STRUCTURE (Lacunar)
Charles François (2004). STRUCTURE (Lacunar), International Encyclopedia of Systems and Cybernetics, 2(2): 3238.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 3238 ▶ |
| Object type | Methodology or model |
In relation to CANTOR's triadic set, M. DUBOIS, P. ATTEN and P. BERGÉ explain as follows the nature of fractal dimensions:
- “The set thus obtained is formed by rigorously ordered points, even if they seem irregularly distributed. Like all fractal objects, this set possesses a lacunar structure, which may be expressed by saying that its dimension is not whole, that it is ”fractal“. It is in no way a curve in view that an infinity of segments are not included. Its dimension is contained between 0 and 1 (0.63…) The same type of structure, in a qualitative sense, is to be found in a transversal section (i.e. a POINCARÉ section of the chaotic attractor constructed by contraction, stretching and folding ad infinitum of a small rectangle in the phases space. These operations transform a segment inside of the rectangle in the phases space into a set of points… whose dimension is also less than 1… As to the attractor it spreads out… in a complex fashion in a three-dimensional space. Its dimension is contained between 2 and 3.” (1987, p.197).