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The design and development of a universal computer in a four-state, five-neighbor cellular model is presented. The underlying structure of the model is an infinite two-dimensional space divided into unit cells each of which can be in one of four states 0, 1, 2, and x. State 0 is the quiescent state, states 1 and 2 are mainly used for signaling, while state x is used for structure purposes. Cells change states at discrete times according to a transition rule which determines the next state of a cell as a function of the present state of the cell itself and its four nondiagonal adjacent neighbors. A configuration is defined to be an assignment of states to all cells in the space such that only a finite number of cells are in the nonquiescent states. A set of configurations, called primitive elements, consisting of the wire, the junction, the corner, the delay, the extendible wire, and the crossover are introduced. Using these elements, a functionally complete set of configurations, called basic organs, comprised of the diode, the OR, the EXCLUSIVE-OR, the clock, and the NOT are developed. The primitive elements and the basic organs are utilized to design four general-purpose components—the encoder, the decoder, the recognizer, and the pulser. These components are used primarily for the detection and the generation of command instructions to and from the universal computer.