scholarly journals Hierarchical self assembly of patterns from the Robinson tilings: DNA tile design in an enhanced Tile Assembly Model

2011 ◽  
Vol 11 (2) ◽  
pp. 323-338 ◽  
Author(s):  
Jennifer E. Padilla ◽  
Wenyan Liu ◽  
Nadrian C. Seeman
Keyword(s):  
Self Assembly ◽  
Assembly Model ◽  
Tile Assembly Model ◽  
Tile Assembly

scholarly journals Self-assembly of 4-sided fractals in the Two-Handed Tile Assembly Model

2018 ◽  
Vol 18 (1) ◽  
pp. 75-92
Author(s):  
Jacob Hendricks ◽  
Joseph Opseth
Keyword(s):  
Self Assembly ◽  
Assembly Model ◽  
Tile Assembly Model ◽  
Tile Assembly

scholarly journals Intrinsic universality and the computational power of self-assembly

2015 ◽  
Vol 373 (2046) ◽  
pp. 20140214 ◽  
Author(s):  
Damien Woods
Keyword(s):  
Self Assembly ◽  
Theoretical Models ◽  
Assembly Model ◽  
Tile Assembly Model ◽  
Intrinsic Universality ◽  
Large Structures ◽  
Large Numbers ◽  
Tile Assembly ◽  
Turing Universality ◽  
Future Work

Molecular self-assembly, the formation of large structures by small pieces of matter sticking together according to simple local interactions, is a ubiquitous phenomenon. A challenging engineering goal is to design a few molecules so that large numbers of them can self-assemble into desired complicated target objects. Indeed, we would like to understand the ultimate capabilities and limitations of this bottom-up fabrication process. We look to theoretical models of algorithmic self-assembly, where small square tiles stick together according to simple local rules in order to carry out a crystal growth process. In this survey, we focus on the use of simulation between such models to classify and separate their computational and expressive powers. Roughly speaking, one model simulates another if they grow the same structures, via the same dynamical growth processes. Our journey begins with the result that there is a single intrinsically universal tile set that, with appropriate initialization and spatial scaling, simulates any instance of Winfree's abstract Tile Assembly Model. This universal tile set exhibits something stronger than Turing universality: it captures the geometry and dynamics of any simulated system in a very direct way. From there we find that there is no such tile set in the more restrictive non-cooperative model, proving it weaker than the full Tile Assembly Model. In the two-handed model, where large structures can bind together in one step, we encounter an infinite set of infinite hierarchies of strictly increasing simulation power. Towards the end of our trip, we find one tile to rule them all: a single rotatable flipable polygonal tile that simulates any tile assembly system. We find another tile that aperiodically tiles the plane (but with small gaps). These and other recent results show that simulation is giving rise to a kind of computational complexity theory for self-assembly. It seems this could be the beginning of a much longer journey, so directions for future work are suggested.

ACTIVE TILE SELF-ASSEMBLY, PART 1: UNIVERSALITY AT TEMPERATURE 1

2014 ◽  
Vol 25 (02) ◽  
pp. 141-163 ◽  
Author(s):  
NATAŠA JONOSKA ◽  
DARIA KARPENKO
Keyword(s):  
Cellular Automata ◽  
Binding Site ◽  
Self Assembly ◽  
Computational Power ◽  
Assembly Model ◽  
Tile Assembly Model ◽  
One Dimensional ◽  
Tile Assembly

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. We also prove that this model has universal computational power in 2D at temperature 1 by showing an active tile assembly construction that simulates one-dimensional cellular automata in 2D at temperature 1.

scholarly journals ASYNCHRONOUS SIGNAL PASSING FOR TILE SELF-ASSEMBLY: FUEL EFFICIENT COMPUTATION AND EFFICIENT ASSEMBLY OF SHAPES

2014 ◽  
Vol 25 (04) ◽  
pp. 459-488 ◽  
Author(s):  
JENNIFER E. PADILLA ◽  
MATTHEW J. PATITZ ◽  
ROBERT T. SCHWELLER ◽  
NADRIAN C. SEEMAN ◽  
SCOTT M. SUMMERS ◽  
...  
Keyword(s):  
Self Assembly ◽  
Fuel Efficiency ◽  
Substantial Improvement ◽  
Efficient Computation ◽  
Assembly Model ◽  
Tile Assembly Model ◽  
High Fuel Efficiency ◽  
Tile Assembly ◽  
Change State ◽  
Assembly Models

In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla et al. [24] to be asynchronous, allowing any action of turning a glue on or off, attaching a new tile, or breaking apart an assembly to happen in any order. Within this highly generalized model we provide three new solutions to tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple complexity metrics. Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models. Our second system of signal-passing tiles simulates any Turing machine with high fuel efficiency by using only a constant number of tiles per computation step. Our third system assembles the discrete Sierpinski triangle, demonstrating that this pattern can be strictly self-assembled within the STAM. This result is of particular interest in that it is known that this pattern cannot self-assemble within a number of well studied tile self-assembly models. Notably, all of our constructions are at temperature 1, further demonstrating that signal-passing confers the power to bypass many restrictions found in standard tile assembly models.

scholarly journals The Two-Handed Tile Assembly Model Is Not Intrinsically Universal

2013 ◽  
pp. 400-412 ◽  
Author(s):  
Erik D. Demaine ◽  
Matthew J. Patitz ◽  
Trent A. Rogers ◽  
Robert T. Schweller ◽  
Scott M. Summers ◽  
...  
Keyword(s):  
Assembly Model ◽  
Tile Assembly Model ◽  
Tile Assembly

Fractal Dimension of Assemblies in the Abstract Tile Assembly Model

2021 ◽  
pp. 116-130
Author(s):  
Daniel Hader ◽  
Matthew J. Patitz ◽  
Scott M. Summers
Keyword(s):  
Fractal Dimension ◽  
Assembly Model ◽  
Tile Assembly Model ◽  
Tile Assembly

scholarly journals Exponential replication of patterns in the signal tile assembly model

2014 ◽  
Vol 14 (2) ◽  
pp. 265-278 ◽  
Author(s):  
Alexandra Keenan ◽  
Robert Schweller ◽  
Xingsi Zhong
Keyword(s):  
Assembly Model ◽  
Tile Assembly Model ◽  
Tile Assembly

One-Time-Pads Encryption in the Tile Assembly Model

2010 ◽  
Vol 7 (5) ◽  
pp. 848-855 ◽  
Author(s):  
Zhihua Chen ◽  
Jin Xu
Keyword(s):  
Assembly Model ◽  
Tile Assembly Model ◽  
Tile Assembly
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