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Working in a three-dimensional variant of Winfree's abstract Tile Assembly Model, we show that, for an arbitrary finite, connected shape $$X \subset \mathbb {Z}^2$$Xi¾?Z2, there is a tile set that uniquely self-assembles into a 3D representation of X at temperature 1 with optimal program-size complexity the program-size complexity, also known as tile complexity, of a shape is the minimum number of tile types required to uniquely self-assemble it. Moreover, our construction is "just barely" 3D in the sense that it only places tiles in the $$z = 0$$z=0 and $$z = 1$$z=1 planes. Our result is essentially a just-barely 3D temperature 1 simulation of a similar 2D temperature 2 result by Soloveichik and Winfree SICOMP 2007.

Optimal Self-assembly of Finite Shapes at Temperature 1 in 3D