The Thue-Morse-Pascal double sequence and similar structures
A recurrent two-dimensional sequence is a function \(a: \mathbb{N}^2 \to A\) with a finite alphabet \(A\) satisfying \(a(i,j) = f(a(i,j-1),a(i-1,j-1),a(i-1,j))\) for some function \(f: A^3 \to A\), for all \(i,j \in \mathbb{N}\). The sequences \(a(k,0)\) and \(a(0,k)\) are called initial conditions. The main theorem states that if a recurrent two-dimensional sequence with initial conditions defined by linear substitutions and a two-dimensional sequence that is generated by a certain type of planar substitutions are identical over a sufficiently large initial square, then they coincide everywhere. Some examples that can be automatically proven using a computer are given. All results are stated without proof in this note.
scientific article; zbMATH DE number 5960867
scientific article