Self-Similar Structure of k- and Biperiodic Fibonacci Words - Bortz, Darby; Cummings, Nicholas; Gao, Suyi; Jaffe, Elias; Mai, Lan; Steinhurst, Benjamin; Tillotson, Pauline (The PUMP Journal of Undergraduate Research, 2024)
Defining the biperiodic Fibonacci words as a class of words over the alphabet 0,1, and two specializations the k-Fibonacci and classical Fibonacci words, we provide a self-similar decomposition of these words into overlapping words of the same type. These self-similar decompositions complement the previous literature where self-similarity was indicated but the specific structure of how the pieces interact was left undiscussed.