Complex Systems and Cognitive Processes
Complex Systems and Cognitive Processes
The mean uncertainty and distance dimension of multidimensional cantorian spaces
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.98 |
We give different descriptions of an abstract n dimensional dynamical system. First, we use a Sierpinski space setting and subsequently we use a statistical cellular space setting. The results of the analysis elucidates certain universal behaviour which was observed in a wide category of cellular automata. The results further show that in four dimensions the phase space dynamics is Peano-like and resembles an Anosov diffeomorphism of a compact manifold which is dense and quasi ergodic. The fractal average distance dimension in this case is d"D^(^4^) = 4.00631 @? 4, and we conjecture that fully developed turbulence is related to d"D^(^5^) = 6.36297. The corresponding Shannon information entropy of the second analysis are S"S^(^4^) = 3.68 and S"S^(^5^) = 6.12. In the case of more-than-seven-dimensional phase space, both descriptions lead to almost identical numerical results. Possible implications of these theoretical results to physical spatio-temporal chaos are discussed.