Related papers: Noncooperative algorithms in self-assembly
In this paper, we introduce the following problem in the theory of algorithmic self-assembly: given an input shape as the seed of a tile-based self-assembly system, design a finite tile set that can, in some sense, uniquely identify whether…
In this paper, we explore relationships between two models of systems which are governed by only the local interactions of large collections of simple components: cellular automata (CA) and the abstract Tile Assembly Model (aTAM). While…
Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…
The emerging field of passive macro-scale tile-based self-assembly (TBSA) shows promise in enabling effective manufacturing processes by harnessing TBSA's intrinsic parallelism. However, current TBSA methodologies still do not fulfill their…
We prove that the abstract Tile Assembly Model (aTAM) of nanoscale self-assembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T.…
Patterned self-assembly is a process whereby coloured tiles self-assemble to build a rectangular coloured pattern. We propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate…
In this paper, we investigate the abilities of systems of self-assembling tiles which can each pass a constant number of signals to their immediate neighbors to create replicas of input shapes. Namely, we work within the Signal-passing Tile…
We present an active tile assembly model which extends Winfree's abstract tile assembly model to tiles that are capable of transmitting and receiving binding site activation signals. In addition, we introduce a mathematical framework to…
Working in Winfree's abstract tile assembly model, we show that a constant-size tile assembly system can be programmed through relative tile concentrations to build an n x n square with high probability, for any sufficiently large n. This…
If particles interact according to isotropic pair potentials that favor multiple length scales, in principle a large variety of different complex structures can be achieved by self-assembly. We present, motivate, and discuss a conjecture…
In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding…
Self-assembly materials are traditionally designed so that molecular or meso-scale components form a single kind of large structure. Here, we propose a scheme to create "multifarious assembly mixtures", which self-assemble many different…
Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…
A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of…
Winfree (1998) showed that discrete Sierpinski triangles can self-assemble in the Tile Assembly Model. A striking molecular realization of this self-assembly, using DNA tiles a few nanometers long and verifying the results by atomic-force…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…
We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et…
We show that in the hierarchical tile assembly model, if there is a producible assembly that overlaps a nontrivial translation of itself consistently (i.e., the pattern of tile types in the overlap region is identical in both translations),…
Since its introduction by Erik Winfree in 1998, the abstract Tile Assembly Model (aTAM) has inspired a wealth of research. As an abstract model for tile based self-assembly, it has proven to be remarkably powerful and expressive in terms of…
We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic or…