Next Article in Journal
Application of Multivariate Empirical Mode Decomposition and Sample Entropy in EEG Signals via Artificial Neural Networks for Interpreting Depth of Anesthesia
Previous Article in Journal
Entropy and Computation: The Landauer-Bennett Thesis Reexamined
Entropy 2013, 15(9), 3312-3324; doi:10.3390/e15093312
Article

On the Entropy of a Two Step Random Fibonacci Substitution

Department of Mathematics, Universität Bielefeld, Postfach 100131, D–33501 Bielefeld, Germany
Received: 8 July 2013 / Revised: 30 July 2013 / Accepted: 19 August 2013 / Published: 23 August 2013
Download PDF [244 KB, uploaded 24 February 2015]

Abstract

We consider a random generalization of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping, a → baa and b → ab, with probability , and  → ba, with probability 1 – p for 0 < p < 1, and where the random rule is applied each time it acts on a . We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words, and we exactly calculate its value.
Keywords: combinatorics on words; asymptotic enumeration; symbolic dynamics combinatorics on words; asymptotic enumeration; symbolic dynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote
MDPI and ACS Style

Nilsson, J. On the Entropy of a Two Step Random Fibonacci Substitution. Entropy 2013, 15, 3312-3324.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here

Comments

Cited By

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert