Staged Self-Assembly and Polyomino Context-Free Grammars
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Staged Self-Assembly and Polyomino Context-Free Grammars Andrew Winslow
description
Staged Self-Assembly and Polyomino Context-Free Grammars. Andrew Winslow. Tile. Glues. Assembly. ×∞. ×∞. ×∞. ×∞. Tile set. M ixing. Bin. Reagents. Products. Size. Staged self-assembly. Three glue types for any shape!. n. How to assemble n-tile stick? . n. - PowerPoint PPT Presentation
Transcript of Staged Self-Assembly and Polyomino Context-Free Grammars
Staged Self-Assembly andPolyomino Context-Free
GrammarsAndrew Winslow
Tile
Glues
Assembly
×∞ ×∞ ×∞ ×∞Tile set
Mixing
Bin
Reagents
Products
Size
Staged self-assembly
Three glue types for any shape!
How to assemble n-tile stick?
n
n≈n size for n-tile stick
n ≈log(n) size for n-tile stick
n
≈n ≈log(n)
Study a simplified model.
Finding small systems is difficult.
Rule
Grammar
#glues2×
Staged System
? ? ?
One dimension
6×
n0.5×
E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, 2011.
Grammar
? ? ?
? ? ? ?
Grammar
Two dimensions
Grammar Staged System
≈n×
log(n)×
? ? ?? ? ?w/scaling
at most ≈log(n)
…
at least ≈n
…
at most ≈log(n)
…
at least ≈n
…
at most ≈log(n)
…
at least ≈n
…
Grammar Staged System
log(n)×
n×
6×
n0.5×
w/scalingThis work
DNA 17
Grammar Staged System
log(n)×
≈n×
6×
n0.5×
w/scaling
Grammars are small,staged systems are always
smaller
Thank you
