{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:32:12Z","timestamp":1760243532364,"version":"build-2065373602"},"reference-count":7,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2013,8,23]],"date-time":"2013-08-23T00:00:00Z","timestamp":1377216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider a random generalization of the classical Fibonacci substitution. The  substitution we consider is defined as the rule mapping, a \u2192 baa and b \u2192 ab, with  probability , and  \u2192 ba, with probability 1 \u2013 p for 0 &lt; p &lt; 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.<\/jats:p>","DOI":"10.3390\/e15093312","type":"journal-article","created":{"date-parts":[[2013,8,23]],"date-time":"2013-08-23T11:38:05Z","timestamp":1377257885000},"page":"3312-3324","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["On the Entropy of a Two Step Random Fibonacci Substitution"],"prefix":"10.3390","volume":"15","author":[{"given":"Johan","family":"Nilsson","sequence":"first","affiliation":[{"name":"Department of Mathematics, Universit\u00e4t Bielefeld, Postfach 100131, D\u201333501 Bielefeld, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2013,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01042590","article-title":"Quasiperiodicity and randomness in tilings of the plane","volume":"55","author":"Luck","year":"1989","journal-title":"J. Stat. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s00605-012-0401-1","article-title":"On the entropy of a family of random substitutions","volume":"168","author":"Nilsson","year":"2012","journal-title":"Monatsh. Math."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Schmid, S., Withers, R.L., and Lifshitz, R. (2013). Aperiodic Crystals, Springer. In press.","DOI":"10.1007\/978-94-007-6431-6"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1951","DOI":"10.1088\/0305-4470\/26\/8\/020","article-title":"The nature of the atomic surfaces of quasiperiodic self-similar structures","volume":"26","author":"Luck","year":"1993","journal-title":"J. Phys. A: Math. Gen."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lind, D., and Marcus, B. (1995). An Introduction to Symbolic Dynamics and Coding, Cambridge University Press.","DOI":"10.1017\/CBO9780511626302"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/BF01504345","article-title":"\u00dcber die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit. ganzzahligen Koeffizienten","volume":"17","author":"Fekete","year":"1923","journal-title":"Math. Zeitschrift"},{"key":"ref_7","unstructured":"Graham, R.L., Knuth, D.E., and Patashnik, O. (1994). Concrete Mathematics, Addison-Wesley Publishing Company."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/9\/3312\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:48:50Z","timestamp":1760219330000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/9\/3312"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,23]]},"references-count":7,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2013,9]]}},"alternative-id":["e15093312"],"URL":"https:\/\/doi.org\/10.3390\/e15093312","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2013,8,23]]}}}