Centralised connectivity-preserving transformations for programmable matter: A minimal seed approach

We study a model of programmable matter systems consisting n devices lying on 2-dimensional square grid which are able to perform the minimal mechanical operation rotating around each other. The goal is transform an initial shape A into target B . investigate class shapes can be constructed in such scenario under additional constraint maintaining global connectivity at all times. focus transforming nice , central line L where for nodes u S either ∈ or connected by perpendicular prove that introducing 3-node seed it possible canonical transformed − 1 nodes. use this show 4-node enables transformation size any other O ( 2 ) time. leave as open problem expansion using include those derived from shapes. • theoretical models systems. One allowed: rotation. Focus transformability questions: given another? With help three convert with constant waste. four via without