Tileassembly

Tileassembly is a framework for self-assembly of square tiles on a two-dimensional grid. Tiles have labeled edges, or glues, that bind to neighboring tiles to form larger structures. The model is used to study computation and programmable matter at the nanoscale.

In the abstract Tile Assembly Model (aTAM), each tile type has four sides with glues. Glues have integer strengths. An assembly starts from a seed tile. A new tile can attach at a site if the sum of the touching glue strengths meets or exceeds a system temperature, τ. This cooperative binding controls growth and, in common variants, tiles attach irreversibly.

Assemblies may be directed (yielding a unique terminal assembly) or nondeterministic. A terminal assembly is one with no possible attachments. Researchers study tile complexity, error resilience, and the range of shapes that can be built.

The aTAM can simulate computation and is considered computationally universal. With appropriate tile sets, it can implement Turing machines and construct shapes encoding computation. This connection underpins experimental work in DNA nanotechnology, where DNA tiles self-assemble into nanoscale structures and circuits. Variants include staged assembly, hierarchical assembly, and probabilistic models.

Tileassembly was introduced by Erik Winfree in the late 1990s and has since become a central framework in algorithmic self-assembly and nanotechnology, inspiring research in theory, design methods, and practical fabrication.