A Brief Tour of Theoretical Tile Self-Assembly

The author gives a brief historical tour of theoretical tile selfassembly via chronological sequence of reports on selected topics in the field. The goal is to provide context and motivation for the these results and the field more broadly. Introduction. This tour covers only a subset of the research topics in theoretical tile self-assembly, listed chronologically according to the most intense interval of study. It is intended for readers who are familiar with the basics of the field and wish to obtain a better understanding of how the multitude of models, problems, and results relate. As such, it is neither a survey nor an introduction; for these, the reader is referred to the excellent works of Doty [18], Patitz [37], Woods [50], and Winfree [47]. Moreover, it does not cover work in experimental DNA tile self-assembly. The aTAM of Winfree (1990s). It is common for work on theoretical tile self-assembly (hereafter tile assembly), to begin “In his Ph.D. thesis, Winfree [47] introduced the abstract tile assembly model (aTAM) . . . ”. The ubiquity of this opener matches the importance this work plays in the field: it is the point of conception, and nearly 20 years later, its reading connotes initiation to the area. Moreover, the sustained popularity of tile assembly is due in large part to the elegance and hidden deoth of this original model. Such intricacy is perhaps most crystallized in a simple yet devious question: is universal computation possible in the aTAM at temperature 1? As with any research, the conception of the aTAM and corresponding experimental implementations were did not occur in isolation. Several other models of (linear) DNA-based computation also introduced around this time,