Line formation and scattering in silent programmable matter

Abstract

Programmable Matter (PM) has been widely investigated in recent years. It refers to some kind of substance with the ability to change its physical properties (e.g., shape or color) in a programmable way. In this paper, we refer to the $\mathrm{SILBOT}$ model, where the particles live and move on a triangular grid, are asynchronous in their computations and movements, and do not possess any direct means of communication (silent) or memory of past events (oblivious).

Within $\mathrm{SILBOT}$, we aim at studying Spanning problems, i.e., problems where the particles are required to suitably span all over the grid. We first address the Line Formation problem where the particles are required to end up in a configuration where they all lie on a line, i.e., they are aligned and connected. Secondly, we deal with the more general Scattering problem: starting from any initial configuration, we aim at reaching a final one where no particles occupy neighboring nodes. Furthermore, we investigate configurations where some nodes of the grid can be occupied by unmovable elements (i.e., obstacles) from both theoretical and experimental view points.