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On Hofstadter Heart Sequences

Author

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  • Altug Alkan
  • Nathan Fox
  • O. Ozgur Aybar

Abstract

The Hofstadter -sequence and the Hofstadter-Conway $10000 sequence are perhaps the two best known examples of meta-Fibonacci sequences. In this paper, we explore an unexpected connection between them. When the -sequence is subtracted from the Conway sequence, a chaotic pattern of heart-shaped figures emerges. We use techniques of Pinn and Tanny et al. to explore this sequence. Then, we introduce and analyze an apparent relative of the -sequence and illustrate how it also generates heart patterns when subtracted from the Conway sequence.

Suggested Citation

  • Altug Alkan & Nathan Fox & O. Ozgur Aybar, 2017. "On Hofstadter Heart Sequences," Complexity, Hindawi, vol. 2017, pages 1-8, November.
    • Handle: RePEc:hin:complx:2614163
    DOI: 10.1155/2017/2614163
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    Cited by:

    1. Trojovský, Pavel, 2020. "On some properties of a meta-Fibonacci sequence connected to Hofstadter sequence and Möbius function," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. 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).

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