The structure of cellular arrays and Tessellation Automata are introduced as a "fabric" for use in the implementation of self-testing and self-repairing computational configurations. Testing schemes are suggested for use in the "self-testing" operation of this computer system. Sequentially propagating tests are examined for both finite and infinite geometries of cellular arrays. A static parallel testing procedure is also suggested which offers these advantages: (1) the parallel testing procedure is transparent to the computer configuration, (2) very little computational down-time" results from testing, and (3) the parallel testing procedure does not initiate reconfiguration of the computational configuration. / Master of Science