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The Power of Seeds in Tile Self-Assembly Andrew Winslow Department of Computer Science, Tufts University.

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Presentation on theme: "The Power of Seeds in Tile Self-Assembly Andrew Winslow Department of Computer Science, Tufts University."— Presentation transcript:

1 The Power of Seeds in Tile Self-Assembly Andrew Winslow Department of Computer Science, Tufts University

2 Abstract Tile Assembly Model (aTAM)

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4 P. W. K. Rothemund, N. Papadakis, E. Winfree, Algorithmic self- assembly of DNA Sierpinski triangles. PLoS Biology (12), Tile Assembly

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18 A Seedless World?

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22 

23 Two-Handed Assembly Model (2HAM)

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26 How powerful is 2HAM relative to aTAM? Are there techniques that require a seed? No.

27 Every aTAM system can be simulated with a 2HAM system.

28 Simulation

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30 Simulation captures dynamics

31 Simulation captures production

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33 Starting the Seed Mortar

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35 Single-Bond Brick & Mortar

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37 Double-Bond Brick &Mortar

38 That simulation is mostly correct…

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40 Interacting Seed Assemblies

41 Inward and Outward Glues Invariant: every exposed glue on an assembly containing a seed is outward.

42 Inward and Outward Glues

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47 Minimal Glue Sets

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52 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.

53 Generalizations

54 Simulating 2HAM dynamics with aTAM? ? Can’t simulate dynamics

55 A Troublesome Shape 

56 A Troublesome Shape 

57 2HAM Binary Counter Counter Tiles

58 2HAM Staircase Assembly Counter Tiles

59  aTAM needs ≈2 b tiles 2HAM needs ≈b tiles b 2 b pillars Can’t simulate production

60 aTAM ≤ 2HAM always Conclusions 2HAM ≤ aTAM at times

61 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


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