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On Some Solutions to Hofstadter's $V$-Recurrence
- Publication Year :
- 2020
-
Abstract
- In this study, we explore the properties of certain solutions of Hofstadter's famous $V$-recurrence, defined by the nested recurrence relation $V(n)=V(n-V(n-1))+V(n-V(n-4))$. First, we discover the nature behind a finite chaotic meta-Fibonacci sequence in terms of mortality in the $V$-recurrence. Then, we construct a new kind of quasi-periodic solution which suggests a connection with another Hofstadter-Huber recursion, $H(n)= H(n-H(n-2)) + H(n-H(n-3))$.
- Subjects :
- Mathematics - Dynamical Systems
Nonlinear Sciences - Chaotic Dynamics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2002.03396
- Document Type :
- Working Paper