On Hofstadter Heart Sequences. (20th November 2017) - Alkan, Altug; Fox, Nathan; Aybar, O. Ozgur
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.