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Self-assembly is one of the prevalent strategies used by living systems to fabricate ensembles of precision nanometer-scale structures and devices. The push for analogous approaches to create synthetic nanomaterials has led to the…

Self-assembly is a process which is ubiquitous in natural, especially biological systems. It occurs when groups of relatively simple components spontaneously combine to form more complex structures. While such systems have inspired a large…

Computational Geometry · Computer Science 2018-07-19 Jerome Durand-Lose , Jacob Hendricks , Matthew J. Patitz , Ian Perkins , Michael Sharp

The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…

Soft Condensed Matter · Physics 2015-06-02 William M. Jacobs , Aleks Reinhardt , Daan Frenkel

Self-closing assembly is prone to polymorphism due to thermally-excited bending fluctuations, which permit the formation of off-target assemblies at the point of self-closure. One way to overcome this source of polymorphism is to use…

Soft Condensed Matter · Physics 2025-11-06 Sirui Liu , Thomas E. Videbæk , W. Benjamin Rogers

The connection between self-assembly and computation suggests that a shape can be considered the output of a self-assembly ``program,'' a set of tiles that fit together to create a shape. It seems plausible that the size of the smallest…

Computational Complexity · Computer Science 2008-06-22 David Soloveichik , Erik Winfree

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,…

Data Structures and Algorithms · Computer Science 2024-08-13 David Furcy , Scott M. Summers

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…

Computational Complexity · Computer Science 2016-10-28 Pierre-Étienne Meunier , Damien Regnault

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…

Computational Complexity · Computer Science 2016-09-08 David Doty , Jack H. Lutz , Matthew J. Patitz , Scott M. Summers , Damien Woods

Controlling the size and shape of assembled structures is a fundamental challenge in self-assembly, and is highly relevant in material design and biology. Here, we show that specific, but promiscuous, short-range binding interactions make…

Soft Condensed Matter · Physics 2025-07-08 Maximilian C. Hübl , Carl P. Goodrich

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…

Computational Complexity · Computer Science 2015-07-31 Pierre-Étienne Meunier , Damien Regnault

Self-assembly is one of the most promising strategies for making functional materials at the nanoscale, yet new design principles for making self-limiting architectures, rather than spatially unlimited periodic lattice structures, are…

The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…

Soft Condensed Matter · Physics 2023-03-13 Joakim Bohlin , Andrew J. Turberfield , Ard A. Louis , Petr Šulc

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…

Discrete Mathematics · Computer Science 2010-03-01 Lila Kari , Shinnosuke Seki , Zhi Xu

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…

Robotics · Computer Science 2022-06-09 M. Jílek , K. Stránská , M. Somr , M. Kulich , J. Zeman , L. Přeučil

Suppose $P$ is a symmetric convex polygon in the plane. We give a polynomial time algorithm that decides if $P$ can tile the plane by transations at some level (not necessarily at level one; this is multiple tiling). The main technical…

Metric Geometry · Mathematics 2020-05-12 Mihail N. Kolountzakis

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…

Computational Geometry · Computer Science 2008-03-04 Erik D. Demaine , Martin L. Demaine , Sandor P. Fekete , Mashhood Ishaque , Eynat Rafalin , Robert T. Schweller , Diane Souvaine

Self-assembly is a fundamental concept in biology and of significant interest to nanotechnology. Significant progress has been made in characterizing and controlling the properties of the resulting structures, both experimentally and…

Soft Condensed Matter · Physics 2024-03-06 Florian M. Gartner , Erwin Frey

We use computational modeling to investigate the assembly thermodynamics of a particle-based model for geometrically frustrated assembly, in which the local packing geometry of subunits is incompatible with uniform, strain-free large-scale…

Soft Condensed Matter · Physics 2021-09-06 Botond Tyukodi , Farzaneh Mohajerani , Douglas M. Hall , Gregory M. Grason , Michael F. Hagan

We ask the question of how small a self-assembling set of tiles can be yet have interesting computational behaviour. We study this question in a model where supporting walls are provided as an input structure for tiles to grow along: we…

Emerging Technologies · Computer Science 2021-06-24 Matthew Cook , Tristan Stérin , Damien Woods

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…

Emerging Technologies · Computer Science 2014-03-10 Jacob Hendricks , Matthew J. Patitz , Trent A. Rogers , Scott M. Summers