Asymmetric bats characterize universality for parallel iteration
Institut für Theoretische Physik, Universität Zürich, CH-8057
2 Institute of Applied Mathematics, Rand Afrikaans University, RSA-2000 Johannesburg, South Africa
Accepted: 30 May 1996
Generalized Baker maps provide one of the most fundamental mechanisms to dynamically generate fractal structures. We show that in the limit of a large number of maps, the entropy function which describes the composed system converges towards a universal entropy function which, qualitatively, depends only on the grammatical structure of the system but has a characteristic bat-like shape. We present theoretical and numerical results on the universal entropy function for different grammars.
PACS: 05.45.+b – Theory and models of chaotic systems / 05.70.Fh – Phase transitions: general aspects / 61.43.Hv – Fractals; macroscopic aggregates (including diffusion-limited aggregates)
© EDP Sciences, 1996