Related papers: Self-Assembly of Patterns in the abstract Tile Ass…
In this paper we propose a research programme for getting structural characterisations for 2-dimensional languages generated by self-assembling tiles. This is part of a larger programme on getting a formal foundation of parallel,…
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…
Nanoparticles with "sticky patches" have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they…
Self-assembly plays an essential role in many natural processes, involving the formation and evolution of living or non-living structures, and shows potential applications in many emerging domains. In existing research and practice, there…
Sequence-directed assembly processes - such as protein folding - allow the assembly of a large number of structures with high accuracy from only a small handful of fundamental building blocks. We aim to explore how efficiently sequence…
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…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…
It is well known that the discrete Sierpinski triangle can be defined as the nonzero residues modulo 2 of Pascal's triangle, and that from this definition one can easily construct a tileset with which the discrete Sierpinski triangle…
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…
We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as…
We study the problem of perfect tiling in the plane and exploring the possibility of tiling a rectangle using integral distinct squares. Assume a set of distinguishable squares (or equivalently a set of distinct natural numbers) is given,…
We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by…
In this paper, we work in a 2D version of the probabilistic variant of Winfree's abstract Tile Assembly Model defined by Chandran, Gopalkrishnan and Reif (SICOMP 2012) in which attaching tiles are sampled uniformly with replacement. First,…
In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
We give an exact formula for the number of distinct square patterns of a given size that occur in the Squiral tiling.
We prove 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 Assembly Model, when restricted to…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
Self-assembled monolayers of microparticles encoding Archimedean and non-regular tessellations promise unprecedented structure-property relationships for a wide spectrum of applications in fields ranging from optoelectronics to surface…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…