Motivated by the idea of describing parquet deformations using grammars and also of describing an infinite number of terminals starting with only a finite set, this paper defines a terminal weighted grammar, where the terminal generated at any step of a derivation is defined as a function of time. It is seen that terminal weighted regular grammars generate exactly the class of recursively enumerable sets. Terminal weighted matrix grammars are used to describe parquet deformations. The extension of terminal weights to array grammars is also discussed. © 1985.