Elements for a theory of fractals in dynamic systems involving human factors

Abstract

The theory which is addressed in this paper is that we should not be surprised to come across fractals in the analysis of some dynamic systems involving human factors. Moreover, in substance, fractals in human behaviour is acceptable. For the convenience of the reader a primary background to some models of fractional Brownian motions which can be found in the literature is given, and then the main features of the complex‐valued model, via a random walk in the complex plane, recently introduced by the author are recalled. The practical meaning of the model is exhibited. The parallel of the central limit theorem here is Levy’s stability. If it is supposed that human decision‐makers work via an observation process which combines the Heisenberg principle and a quantization principle in the measurement, then fractal dynamics appears to be quite in order. The relation with the theory of relative information is exhibited. The conjecture is then the following: could this model explain why fractals appear in finance, for instance?

Citation

Jumarie, G. (1999), "Elements for a theory of fractals in dynamic systems involving human factors", Kybernetes, Vol. 28 No. 4, pp. 407-422. https://doi.org/10.1108/03684929910267743