Geometric tiles and powers and limitations of geometric hindrance in self-assembly

Tile-based self-assembly systems are capable of universal computation and algorithmically directed growth. Systems such behaviors typically make use “glue cooperation” in which the glues on at least 2 sides a tile must match bind to those exposed perimeter an assembly for that attach. However, several models have been developed utilize “weak cooperation”, where only single glue needs but other preventative forces (such as geometric, or steric, hindrance) provide additional selection tiles may attach, this allows algorithmic behavior. In paper we first work model allowed geometric bumps dents their edges. We show how “geometric” can simulate square with complex functions (using asymptotically optimal sizes dents). then scale factor 1 it is impossible behavior include duples (i.e. either twice long tall tiles), also weak cooperation via hindrance, no system any even class tightly constrained, deterministic cooperative systems. This helps further define limits powers relying hindrance instead cooperation.A shortened version appeared proceedings 18th International Conference Unconventional Computation Natural (UCNC 2019).