On Hofstadter Heart Sequences. (20th November 2017)

• Record Type: Journal Article
• Authors: Alkan, Altug; Fox, Nathan; Aybar, O. Ozgur
• Other Names: Giesl Peter Academic Editor.
• Is Part Of: Complexity. Volume 2017(2017)
• Publication Date: 2017-11-20
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2017/2614163
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : The Hofstadter Q -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 Q -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 Q -sequence and illustrate how it also generates heart patterns when subtracted from the Conway sequence.