Fibonacci Sequences of 1D, 2D Words: Enumerating and Locating the Factors of the Fixed Points

Abstract

Given an infinite word, enumerating its factors is an important exercise for understanding the structure of the word. The process of finding all the factors is quite tricky for two-dimensional words. In this paper, two possible ways of enumerating the factors of the fixed point ($f_{\infty,\infty}$) of the sequence of Fibonacci arrays and a method for locating these factors in $f_{\infty,\infty}$ are explored. In addition, the factor complexity and the locations of the factors of the fixed point of Fibonacci sequence of arrays are also analysed.