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An exploration of solutions to two related Hofstadter-Huber recurrence relations

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  • Alkan, Altug
  • Fox, Nathan
  • Aybar, Orhan Ozgur
  • Akdeniz, Zehra

Abstract

In this study, we explore the properties of certain solutions of two Hofstadter-Huber recurrence relations. The first is Hofstadter’s V-recurrence, which is defined by the nested recurrence relation V(n)=V(n−V(n−1))+V(n−V(n−4)). Plus, we introduce another meta-Fibonacci recurrence H(n)=H(n−H(n−2))+H(n−H(n−3)). First, we study a finite chaotic solution to the V-recurrence in order to analyse its generational structure. Then, we explore a new type of infinite solution to nested recurrence relations, finding solutions of this type to both the V-recurrence and the H-recurrence. Our construction relates to systems of nested recurrences that resemble Golomb’s recurrence G(n)=G(n−G(n−1))+1.

Suggested Citation

  • Alkan, Altug & Fox, Nathan & Aybar, Orhan Ozgur & Akdeniz, Zehra, 2020. "An exploration of solutions to two related Hofstadter-Huber recurrence relations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303003
    DOI: 10.1016/j.chaos.2020.109900
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    References listed on IDEAS

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    1. Altug Alkan & Nathan Fox & O. Ozgur Aybar, 2017. "On Hofstadter Heart Sequences," Complexity, Hindawi, vol. 2017, pages 1-8, November.
    2. Altug Alkan, 2018. "On a Generalization of Hofstadter’s -Sequence: A Family of Chaotic Generational Structures," Complexity, Hindawi, vol. 2018, pages 1-8, June.
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