A highly parallel machine is, in concept, a multiprocessor with more than one hundred semi-independent, program-controlled computing elements. One type of highly parallel machine is the parallel-network computer, wherein the computing elements are arranged in a geometrical array and direct communication among elements is restricted for each to a local neighborhood. (See Section II.) Most of the postulated network systems have a separate central control unit that directs the operation of the network. Examples of such are Unger's machine (References 17 and 18), McCormick's machine (References 5 and 13), and SOLOMON (References 1, 14, and 15). The only published example of a network machine without central control is that proposed by Holland (References 4, 9, 10, and 16), and is the organization to be considered here.