On the Entropy of a Two Step Random Fibonacci Substitution
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 sho...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2013-08-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/15/9/3312 |
| _version_ | 1818013644496044032 |
|---|---|
| author | Johan Nilsson |
| author_facet | Johan Nilsson |
| author_sort | Johan Nilsson |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T06:35:50Z |
| format | Article |
| id | doaj.art-cb839088e86d4bddb7b888cf823d98a5 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T06:35:50Z |
| publishDate | 2013-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-cb839088e86d4bddb7b888cf823d98a52022-12-22T02:07:28ZengMDPI AGEntropy1099-43002013-08-011593312332410.3390/e15093312On the Entropy of a Two Step Random Fibonacci SubstitutionJohan NilssonWe 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.http://www.mdpi.com/1099-4300/15/9/3312combinatorics on wordsasymptotic enumerationsymbolic dynamics |
| spellingShingle | Johan Nilsson On the Entropy of a Two Step Random Fibonacci Substitution Entropy combinatorics on words asymptotic enumeration symbolic dynamics |
| title | On the Entropy of a Two Step Random Fibonacci Substitution |
| title_full | On the Entropy of a Two Step Random Fibonacci Substitution |
| title_fullStr | On the Entropy of a Two Step Random Fibonacci Substitution |
| title_full_unstemmed | On the Entropy of a Two Step Random Fibonacci Substitution |
| title_short | On the Entropy of a Two Step Random Fibonacci Substitution |
| title_sort | on the entropy of a two step random fibonacci substitution |
| topic | combinatorics on words asymptotic enumeration symbolic dynamics |
| url | http://www.mdpi.com/1099-4300/15/9/3312 |
| work_keys_str_mv | AT johannilsson ontheentropyofatwosteprandomfibonaccisubstitution |