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nth order Fibonacci word fn is defined recursively by fixing the first two initial letters, namely f0 and f1. W.H. Chaun (1993) proposed a few ways of indexing the Fibonacci words with binary sequences in order to generate the Fibonacci words. Two-dimensional Fibonacci words (or Fibonacci arrays) were first defined in the year 2000 as an infinite sequence of arrays obtained recursively by fixing the four initial letters, namely f0,0, f0,1, f1,0 and f1,1. In 2021, few results on indexed Fibonacci and indexed involutive Fibonacci words have been studied. In this paper, we extend their work to Fibonacci arrays by defining a new way of indexing and proving results based on the indexing. [ABSTRACT FROM AUTHOR]

In this paper, we put forward models that generate two-dimensional palindromic languages with array-rewriting rules. The rewriting rules are of either regular or context-free type with terminals being arrays. The derivation lengths are managed by the array concatenation conditions. These grammars give rise to an extensive variety of palindromic pictures. Different hierarchies that exist between the classes defined are demonstrated. The closure properties have also been evaluated. Applications of these models have been explored by generating a few patterns of kolams. [ABSTRACT FROM AUTHOR]

Various scholars have investigated Fibonacci arrays to uncover its combinatorial features and applications. As an extension of Involutive Fibonacci words, Involutive Fibonacci arrays were introduced. We will look at some of the combinatorial features of Involutive Fibonacci Arrays in this article. [ABSTRACT FROM AUTHOR]