We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile as...
Molecular self-assembly is a promising approach to bottom-up fabrication of complex structures. A major impediment to the practical use of self-assembly to create complex structure...
We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile...
David Doty, Jack H. Lutz, Matthew J. Patitz, Scott...
We consider the problem of tiling a segment {0, . . . , n} of the discrete line. More precisely, we ought to characterize the structure of the patterns that tile a segment and thei...
A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings ar...