2021/08/20 by Matthew P. Connor, Connor, Matthew, Othon Michail +3
Engineering · Physics and Astronomy · #Advanced Materials and Mechanics #Distributed #FOS: Computer and information sciences #Micro and Nano Robotics #Modular Robots and Swarm Intelligence #Parallel #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2108.09250
openalex publication_date 2021/08/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We study a model of programmable matter systems consisting of n devices lying on a 2-dimensional square grid which are able to perform the minimal mechanical operation of rotating around each other. The goal is to transform an initial shape A into a target shape B. We investigate the class of shapes which can be constructed in such a scenario under the additional constraint of maintaining global connectivity at all times. We focus on the scenario of transforming nice shapes, a class of shapes consisting of a central line L where for all nodes u in S either u ∈ L or u is connected to L by a line of nodes perpendicular to L. We prove that by introducing a minimal 3-node seed it is possible for the canonical shape of a line of n nodes to be transformed into a nice shape of n-1 nodes. We use this to show that a 4-node seed enables the transformation of nice shapes of size n into any other nice shape of size n in O(n2) time. We leave as an open problem the expansion of the class of shapes which can be constructed using such a seed to include those derived from nice shapes.