Self-Similar Structure of k- and Biperiodic Fibonacci Words

  • Darby Bortz Washington County Public Schools
  • Nicholas Cummings Tufts University
  • Suyi Gao Purdue University
  • Elias Jaffe Acclaim Technical Services
  • Lan Mai University of Delaware
  • Benjamin Steinhurst McDaniel College
  • Pauline Tillotson McDaniel College
Keywords: fractals; Fibonacci words; biperiodic Fibonacci words; L-systems; iterated function systems


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.

How to Cite
Bortz, D., Cummings, N., Gao, S., Jaffe, E., Mai, L., Steinhurst, B., & Tillotson, P. (2024). Self-Similar Structure of k- and Biperiodic Fibonacci Words. The PUMP Journal of Undergraduate Research, 7, 1-13.