Related papers: Scaled tree fractals do not strictly self-assemble

In this paper we define the Dupled abstract Tile Assembly Model (DaTAM), which is a slight extension to the abstract Tile Assembly Model (aTAM) that allows for not only the standard square tiles, but also "duple" tiles which are rectangles…

The field of algorithmic self-assembly is concerned with the computational and expressive power of nanoscale self-assembling molecular systems. In the well-studied cooperative, or temperature 2, abstract tile assembly model it is known that…

We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by…

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 assembly system. We give a tile assembly system that is…

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…

We define the Reflexive Tile Assembly Model (RTAM), which is obtained from the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across their horizontal and/or vertical axes. We show that the class of directed temperature-1…

Self-assembly is ubiquitous in nature, particularly in biology, where it underlies the formation of protein quaternary structure and protein aggregation. Quaternary structure assembles deterministically and performs a wide range of…

In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types…

Behaviors of Winfree's tile assembly systems (TASs) at high temperatures are investigated in combination with integer programming of a specific form called threshold programming. First, we propose a way to build bridges from the Boolean…

We prove that the number of tile types required to build squares of size n x n, in Winfree's abstract Tile Assembly Model, when restricted to using only non-cooperative tile bindings, is at least 2n-1, which is also the best known upper…

We investigate a fundamental question regarding a benchmark class of shapes in one of the simplest, yet most widely utilized abstract models of algorithmic tile self-assembly. Specifically, we study the directed tile complexity of a $k…

We prove that if a subset X of the integer Cartesian plane weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as *pumpability*, then X is a finite union of doubly…

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…

We investigate the power of the Wang tile self-assembly model at temperature 1, a threshold value that permits attachment between any two tiles that share even a single bond. When restricted to deterministic assembly in the plane, no…

We consider the problem of fault-tolerance in nanoscale algorithmic self-assembly. We employ a variant of Winfree's abstract Tile Assembly Model (aTAM), the two-handed aTAM, in which square "tiles" -- a model of molecules constructed from…

We consider the tile self-assembly model and how tile complexity can be eliminated by permitting the temperature of the self-assembly system to be adjusted throughout the assembly process. To do this, we propose novel techniques for…

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 assembly systems in which shapes and patterns that represent…

We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…

In the abstract Tile Assembly Model (aTAM) square tiles self-assemble, autonomously binding via glues on their edges, to form structures. Algorithmic aTAM systems can be designed in which the patterns of tile attachments are forced to…

We prove a result which strongly hints at the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile…