On the Entropy of a Two Step Random Fibonacci Substitution

Johan Nilsson

doi:10.3390/e15093312

paper

On the Entropy of a Two Step Random Fibonacci Substitution

arXiv:1303.2526 · doi:10.3390/e15093312

Abstract

We consider a random generalisation of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping $a \mapsto baa$ and $b \mapsto ab$ with probability $p$ and $b \mapsto ba$ with probability $1 - p$ for $0 < p < 1$ and where the random rule is applied each time it acts on a $b$ . 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.

16 pages

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Magic numbers in the discrete tomography of cyclotomic model sets

On the Entropy of a Two Step Random Fibonacci Substitution

Abstract

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