Tile SelfAssembly Andrew Winslow Department of Computer Science Tufts University Abstract Tile Assembly Model aTAM Abstract Tile Assembly Model aTAM P W K Rothemund N Papadakis ID: 576802
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Slide1
The Power of Seeds in Tile Self-Assembly
Andrew WinslowDepartment of Computer Science, Tufts UniversitySlide2
Abstract Tile Assembly Model (
aTAM
)Slide3
Abstract Tile Assembly Model (aTAM)Slide4
P. W. K.
Rothemund, N.
Papadakis, E. Winfree, Algorithmic self-assembly of DNA Sierpinski triangles. PLoS
Biology (12), 2004.
Tile AssemblySlide5
Tile AssemblySlide6
Tile AssemblySlide7
Tile AssemblySlide8
Tile AssemblySlide9
Tile AssemblySlide10
Tile AssemblySlide11
Tile AssemblySlide12
Tile AssemblySlide13
Tile AssemblySlide14
Tile AssemblySlide15
Tile AssemblySlide16
Tile AssemblySlide17Slide18
A Seedless World?Slide19
A Seedless World?Slide20
A Seedless World?Slide21
A Seedless World?Slide22
A Seedless World?
Slide23
Two-Handed Assembly Model (2HAM)Slide24
Two-Handed Assembly Model (2HAM)Slide25
Two-Handed Assembly Model (2HAM)Slide26
How powerful is 2HAM relative to
aTAM?
Are there techniques that require a seed?
No.Slide27
Every
aTAM system can be simulated
with a 2HAM system.Slide28
SimulationSlide29
SimulationSlide30
Simulation captures
dynamicsSlide31
Simulation captures
productionSlide32Slide33
Starting the Seed MortarSlide34Slide35
Single-Bond Brick & MortarSlide36Slide37
Double-Bond Brick &MortarSlide38
That simulation is
mostly correct…Slide39Slide40
Interacting Seed AssembliesSlide41
Inward and Outward Glues
Invariant: every exposed glue on an
assembly containing a seed is outward.Slide42
Inward and Outward GluesSlide43Slide44Slide45Slide46Slide47
Minimal Glue SetsSlide48
Minimal Glue SetsSlide49
Minimal Glue SetsSlide50
Minimal Glue SetsSlide51
Minimal Glue SetsSlide52
Preventing Seed Assembly Interaction
Idea #1: maintain that all exposed glues on any seed assembly are outward glues.
Idea #2: ensure every attaching brick uses all inward glues to attach, leaving only outward glues exposed. Slide53
Generalizations Slide54
Simulating 2HAM dynamics with
aTAM
?
?
Can’t simulate dynamicsSlide55
A Troublesome Shape
Slide56
A Troublesome Shape
Slide57
2HAM Binary Counter
Counter Tiles
Counter Tiles
Counter TilesSlide58
2HAM Staircase Assembly
Counter TilesSlide59
aTAM
needs ≈2
b
tiles
2HAM needs ≈
b
tiles
b
2
b
pillars
Can’t simulate productionSlide60
aTAM
≤ 2HAM always
Conclusions
2HAM ≤ aTAM at timesSlide61
Acknowledgements
Joint work with:
Sarah Cannon, Erik and Martin Demaine, Sarah
Eisenstat, Matthew Patitz, Robert
Schweller, and Scott Summers.
Research funded in part by NSF grant CBET-0941538