Many complex natural and man made systems are inherently concurrent in nature, consisting of many autonomous parts that interact with each other. Cellular automata allow the concurrency and interactions of these complex systems to be modelled. Using a reconfigurable a computing platform for running cellular automata models allows the natural concurrency of digital electronics to be directly exploited by the system being modelled. This thesis investigates methods and philosophies for developing cellular automata models on a reconfigurable computing platform, the SPACE machine. Modelling and verification techniques are developed using a process algebra, Circal. These techniques allow the desired behaviour of a system to be specified and simulated. The model is then translated into a digital design, which can be verified as correct against the behavioural model using the Circal system. Three cellular automata system are used to develop the methods and philosophies. The Game of Life is used to investigate how to model and implement CA on the SPACE machine. The Philosophies and techniques that are developed for the Game of Life are used in the following systems. More complex cellular automata models of road traffic are used to further develop the modelling techniques developed in the Game a Life. A user interface, which was created for viewing the outputs from the Game a Life, is extended to allow cellular automata cells to be dynamically placed and moved about on the computing surface, allowing the user to observe and modify experiment in real time. A cellular automata based cryptography system is then used to further enhance the techniques developed, and particularly to explore the area of producing dynamically reconfigured circuits as the inputs to the system change. The thesis concludes that there are many real life complex systems, such as road traffic simulation and cryptography, which require high performs systems to run on. The methods and philosophies developed in this thesis allow CA systems to be modelled using process algebra and run directly in digital hardware, allowing the natural concurrency of the hardware to be fully exploited.