Self-organizing formation algorithm for active elements

We propose a novel method of self-organizing formation. It is assumed that elements are not connected to each other and they can move in continuous space. The objective is to arrange elements in a certain spatial pattern like a crystal, and to make the outline of the group in the desired shape. For this purpose, we propose a method by using virtual springs among the elements. In this algorithm, an element generates virtual springs between the neighbor element based on information of how many other elements exist in the neighborhood with a certain radius. Although the elements interact locally, only by virtual springs, and they do not have global information at all, they form a shape much larger than the sensory radius. By a simulation study, we confirmed convergence to a target shape from a random state in very high probability. This kind of algorithm gives a new principle of self-organizing formation, and its simplicity will be useful for the design of self-assembling nano machines in future.