2012/12/06 by Jósé L. Ramírez, José L. Ramírez, Gustavo N. Rubiano +6
Computer Science · Mathematics · #05B50 #11B39 #28A80 #68R15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Dynamics and Fractals #cs.DM #math.CO #msc:05B50 #msc:11B39 #msc:28A80 #msc:68R15 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1212.1368
openalex publication_date 2012/12/06 · arxiv created 2014/02/04 · arxiv updated 2014/02/05 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. Moreover, we associate to this family of words a family of curves, which have fractal properties, in particular these curves have as attractor the Fibonacci word fractal. Finally, we describe an infinite family of polyominoes (double squares) from the generalized Fibonacci words and we study some of their geometric properties. These last polyominoes generalize the Fibonacci snowflake.