Formal properties of sequential/parallel matrix languages

A new type of grammar for generating two-dimensional patterns is introduced. The generation of a pattern occurs in two phases. First, a string grammar generates a “row” of syntactic variables (the sequential phase). Then a battery of instances of string grammars—one for each symbol produced in the first phase—operate in tandem to create the columns of the final pattern (the parallel phase). Several unrelated properties of the classes of patterns generated by various varieties of matrix grammars are announced.