Self-Assembly Of And Optimal Encoding Within Thin Rectangles At Temperature-1 In 3d

In this paper, we study the self-assembly of rectangles in a non-cooperative, 3D version of Winfree's abstract Tile Assembly Model. We prove two results. First, we give the full details for the proof of a general construction for the efficient self-assembly of thin rectangles that was first reported by Furcy, Summers and Wendlandt (2019). This construction is noncooperative and "just-barely" 3D in the sense that it places tiles at most one step into the third dimension. Second, we give a non-cooperative, just-barely 3D optimal encoding construction that self-assembles the bits of a given binary string along the perimeter of a thin rectangle of constant height. (C) 2021 Elsevier B.V. All rights reserved.