On a generalization of Hofstadter's \(Q\)-sequence: a family of chaotic generational structures
type: Item
instance of: scholarly article
title: On a generalization of Hofstadter's \(Q\)-sequence: a family of chaotic generational structures
zbMATH Open document ID: 1398.11032
DOI: 10.1155/2018/8517125
author: Altug Alkan
published in: Complexity
publication date: 2018-09-27T00:00:00Z
review text: Summary: Hofstadter \(Q\)-recurrence is defined by the nested recurrence \(Q \left(n\right) = Q \left(n - Q \left(n - 1\right)\right) + Q \left(n - Q \left(n - 2\right)\right)\), and there are still many unanswered questions about certain solutions of it. In this paper, a generalization of Hofstadter's \(Q\)-sequence is proposed and selected members of this generalization are investigated based on their chaotic generational structures and Pinn's statistical technique. Solutions studied have also curious approximate patterns and considerably similar statistical properties with Hofstadter's famous \(Q\)-sequence in terms of growth characteristics of their successive generations. In fact, the family of sequences that this paper introduces suggests the existence of conjectural global properties in order to classify unpredictable solutions to \(Q\)-recurrence and a generalization of it.
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 6944921
zbMATH Keywords: Hofstadter's \(Q\)-sequence
zbMATH Keywords: chaotic generational structures
Wikidata QID: Q60692614
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8517125
OpenAlex ID: W2810104609
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DBLP publication ID: journals/complexity/Alkan18
description: scientific article; zbMATH DE number 6944921