On Hofstadter Heart Sequences

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.

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