1. A triple-folded array parallel computing system comprising: a plurality of processing elements (PEs) each coupled to a plurality of others of said PEs such that the plurality of PEs is logically equivalent to at least a square two dimensional array configuration of PEs having an equal number of PE's as said computing system, for executing at least algorithms executable on the two dimensional array configuration; each of the PEs comprising: a plurality of I/O ports for sending and receiving instructions and data to and from coupled ones of the PEs, means for executing instructions, and means for storing instructions and data; a portion of the PEs paired by a first diagonal fold in said square array into a plurality of symmetric PEs forming a first fold mesh, the symmetric PEs each comprising a pair of a first PE and a second PE sharing each of said I/O ports as shared ports for sending and receiving instructions and data such that each of the pair of PEs communicates with PEs originally coupled to the first PE and with PEs originally coupled to the second PE of said pair of PEs, said pair of PEs including PE.sub.ij and PE.sub.ji, where i and j are column and row designators of a PE in said logically equivalent square two dimensional array configuration, and where i and j are positive non-equal integers; a remaining portion of the PEs configured into a plurality of diagonal PEs, the diagonal PEs each coupled to two symmetric PEs each via one of said shared ports; and said plurality of symmetric PEs and diagonal PEs grouped by consecutive second and third folds in said first fold mesh, into a plurality of clusters each comprising a plurality of PEs, a portion of the clusters each comprising four symmetric PEs and a remaining portion of the clusters each comprising two diagonal PEs, the plurality of clusters each comprising an additional coupling between a pair of previously uncoupled PEs.