scholarly journals On the Equivalence of Cellular Automata and the Tile Assembly Model

2013 ◽  
Vol 128 ◽  
pp. 167-189 ◽  
Author(s):  
Jacob Hendricks ◽  
Matthew J. Patitz
Keyword(s):  
Cellular Automata ◽  
Assembly Model ◽  
Tile Assembly Model ◽  
Tile Assembly

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 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

scholarly journals The Tile Assembly Model is Intrinsically Universal

2012 ◽  
Author(s):  
David Doty ◽  
Jack H. Lutz ◽  
Matthew J. Patitz ◽  
Robert T. Schweller ◽  
Scott M. Summers ◽  
...  
Keyword(s):  
Assembly Model ◽  
Tile Assembly Model ◽  
Tile Assembly
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