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

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Presentation transcript:

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

Abstract Tile Assembly Model (aTAM)

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

A Seedless World?



Two-Handed Assembly Model (2HAM)

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

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

Simulation

Simulation captures dynamics

Simulation captures production

Starting the Seed Mortar

Single-Bond Brick & Mortar

Double-Bond Brick &Mortar

That simulation is mostly correct…

Interacting Seed Assemblies

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

Inward and Outward Glues

Minimal Glue Sets

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.

Generalizations

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

A Troublesome Shape 

A Troublesome Shape 

2HAM Binary Counter Counter Tiles

2HAM Staircase Assembly Counter Tiles

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

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

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