On a Generalization of Hofstadter's Q-Sequence: A Family of Chaotic Generational Structures

Abstract

Hofstadter Q-recurrence is defined by the nested recurrence Q(n) = Q(n - Q(n - 1)) + Q(n - Q(n - 2)), and there are still many unanswered questions about certain solutions of it. In this paper, a generalization of Hofstadter's Q-sequence is proposed and selected members of this generalization are investigated based on their chaotic generational structures and Pinn's statistical technique. Solutions studied have also curious approximate patterns and considerably similar statistical properties with Hofstadter's famous Q-sequence in terms of growth characteristics of their successive generations. In fact, the family of sequences that this paper introduces suggests the existence of conjectural global properties in order to classify unpredictable solutions to Q-recurrence and a generalization of it.