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Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks, to hierarchical sequences of intermediates, all the way to the fully…

Soft Condensed Matter · Physics 2015-08-12 Jim Madge , Mark A. Miller

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…

Computational Complexity · Computer Science 2013-12-10 Pierre-Étienne Meunier

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…

Emerging Technologies · Computer Science 2012-11-14 Natasha Jonoska , Daria Karpenko

We investigate motion planning algorithms for the assembly of shapes in the \emph{tilt model} in which unit-square tiles move in a grid world under the influence of uniform external forces and self-assemble according to certain rules. We…

Robotics · Computer Science 2023-07-07 Patrick Blumenberg , Arne Schmidt , Aaron T. Becker

Algorithmic self-assembly occurs when disorganized components autonomously combine to form structures and, by their design and the dynamics of the system, are forced to follow the execution of algorithms. Motivated by applications in…

Computational Geometry · Computer Science 2023-05-05 Daniel Hader , Matthew J. Patitz

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…

Data Structures and Algorithms · Computer Science 2013-01-15 Damien Woods , Ho-Lin Chen , Scott Goodfriend , Nadine Dabby , Erik Winfree , Peng Yin

Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA)…

Emerging Technologies · Computer Science 2019-06-06 John Calvin Alumbaugh , Joshua J. Daymude , Erik D. Demaine , Matthew J. Patitz , Andrea W. Richa

This paper explores the use of negative (i.e., repulsive) interaction the abstract Tile Assembly Model defined by Winfree. Winfree postulated negative interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu, and Yin…

Data Structures and Algorithms · Computer Science 2015-05-18 David Doty , Lila Kari , Benoit Masson

Self-assembly kinetics is usually described by approaches which assume that the shape of the aggregates has a definite form (e.g., spherical, cylindrical, cubic, etc), however that is unlikely to be the case in many finite-sized…

Soft Condensed Matter · Physics 2022-07-13 L. F. Trugilho , L. G. Rizzi

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…

Computational Geometry · Computer Science 2021-02-03 Andreas M. Tillmann , Leif Kobbelt

This paper introduces a method to generate highly selective encodings that can be magnetically "programmed" onto physical modules to enable them to self-assemble in chosen configurations. We generate these encodings based on Hadamard…

Robotics · Computer Science 2022-08-09 Martin Nisser , Yashaswini Makaram , Faraz Faruqi , Ryo Suzuki , Stefanie Mueller

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

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

We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. While previous work within this model of assembly has focused on…

We consider methods for connected reconfigurations by finite automate in the so-called \emph{hybrid} or \emph{Robot-on-Tiles} model of programmable matter, in which a number of simple robots move on and rearrange an arrangement of passive…

Computational Geometry · Computer Science 2019-09-10 Sándor P. Fekete , Eike Niehs , Christian Scheffer , Arne Schmidt

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…

Emerging Technologies · Computer Science 2022-11-10 Andrew Alseth , Matthew J. Patitz

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.…

Data Structures and Algorithms · Computer Science 2012-04-10 David Doty , Jack H. Lutz , Matthew J. Patitz , Robert T. Schweller , Scott M. Summers , Damien Woods

The simulated self-assembly of molecular building blocks into functional complexes is a key area of study in computational biology and materials science. Self-assembly simulations of proteins using physically-motivated potentials for…

Soft Condensed Matter · Physics 2025-09-03 Ivan Spirandelli , Arnur Nigmetov , Dmitriy Morozov , Myfanwy E. Evans

We present a strict separation between the class of "mismatch free" self-assembly systems and general aTAM systems. Mismatch free systems are those systems in which concurrently grown parts must always agree with each other. Tile…

Computational Geometry · Computer Science 2015-02-20 Florent Becker , Pierre-Étienne Meunier

Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…

Soft Condensed Matter · Physics 2026-02-13 P. D. S. de Lima , R. De La Cour , K. Gaff , J. M. de Araújo , S. J. Cox , M. S. Ferreira , S. Hutzler