The Power of Seeds in Tile Self-Assembly
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Transcript of The Power of Seeds in Tile Self-Assembly
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The Power of Seeds in Tile Self-Assembly
Andrew WinslowDepartment of Computer Science, Tufts University
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Abstract Tile Assembly Model (aTAM)
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Abstract Tile Assembly Model (aTAM)
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P. W. K. Rothemund, N. Papadakis, E. Winfree, Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biology (12), 2004.
Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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Tile Assembly
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A Seedless World?
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A Seedless World?
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A Seedless World?
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A Seedless World?
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A Seedless World?
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Two-Handed Assembly Model (2HAM)
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Two-Handed Assembly Model (2HAM)
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Two-Handed Assembly Model (2HAM)
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How powerful is 2HAM relative to aTAM?
Are there techniques that require a seed?
No.
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Every aTAM system can be simulated with a 2HAM system.
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Simulation
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Simulation
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Simulation captures dynamics
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Simulation captures production
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Starting the Seed Mortar
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Single-Bond Brick & Mortar
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Double-Bond Brick &Mortar
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That simulation is mostly correct…
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Interacting Seed Assemblies
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Inward and Outward Glues
Invariant: every exposed glue on an assembly containing a seed is outward.
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Inward and Outward Glues
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Minimal Glue Sets
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Minimal Glue Sets
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Minimal Glue Sets
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Minimal Glue Sets
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Minimal Glue Sets
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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.
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Generalizations
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Simulating 2HAM dynamics with aTAM?
? Can’t simulate dynamics
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A Troublesome Shape
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A Troublesome Shape
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2HAM Binary Counter
Counter TilesCounter TilesCounter Tiles
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2HAM Staircase Assembly Counter Tiles
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aTAM needs ≈2b tiles2HAM needs ≈b tiles
b
2b pillars
Can’t simulate production
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aTAM ≤ 2HAM always
Conclusions
2HAM ≤ aTAM at times
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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