Fast, Long-Range Synchronization Utilizing Emergents: Proof of Concept and Prospective Applications of Emergent Computing

So far, synchronization tasks designed in complex systems are working at the level of their constituting elements. The proposed pilot study explores synchronization at the level of emergents. The main objective of this research is threefold: (i) to demonstrate that synchronizing emergent structures rise from a continuous interaction of micro-processes that are operating above a constituting matrix (medium) using a simple microevolution rule and a special type of extended neighborhood; (ii) to provide a specific example of a long-range emergent coordination that is generated within a short-range communicating medium; and (iii) to demonstrate a possibility of synchronization at the level of emergents. Those goals are achieved by the utilization of emergent information processing that uses uniform changes of all updated elements of the matrix, a fixed microevolution rule, and a fixed neighborhood. A fast solution to a computational problem of solving long-range synchronization within massively parallel and short-range communicating environments is presented. It is named the semi-two-dimensional synchronization problem (S2D-SP). The proposed emergent solution of S2D-SP differs from all previous manually designed solutions to other synchronization tasks. The number of steps t, which is necessary to synchronize an emergent array, is substantially lower than the width w of the synchronized emergent array. In addition to the pure theoretical importance, the solution demonstrates the usefulness of the concept of extended neighborhoods in search of not only biologically relevant computational models of self-organization and emergence. The presented solution of the S2D-SP problem uncovers a novel approach to the design of artificial, self-organizing emergent systems and possibly paves a path towards understanding natural computation. The software GoL-N24 v1.4 used to generate all results is publicly available.