Cellular automata is a nature inspired parallel processing model. It has been proposed several years ago by J. Von Neumann to simulate complex dynamical processes. In the past two decades several models of cellular automata that differ from the original one proposed by Von Neumann have been defined for modeling real-world systems and phenomena. This paper describes the design and implementation of standard and nonstandard parallel cellular automata in the CARPET language. CARPET is a cellular automata based language that has been implemented on MIMD parallel computers. The language is specifically designed for programming cellular computations supporting concise and efficient coding of parallel cellular algorithms. The paper analyzes the main features of the language and describes as they can be exploited to implement different cellular automata on parallel computers, starting from the standard model to its modifications and generalizations. Inhomogeneous, partitioned, asynchronous, and probabilistic cellular automata programmed in CARPET are presented.