On Hofstadter Heart Sequences

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.