Difference between revisions of "Quantifying progress by scaling in achievable complexity"
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Calculating the exact number of accessible states can quickly become very difficult to impossible. <br> | Calculating the exact number of accessible states can quickly become very difficult to impossible. <br> | ||
Upper and lower bound estimates beyond the most naive approaches can be accessible though. <br> | Upper and lower bound estimates beyond the most naive approaches can be accessible though. <br> | ||
| − | Then a geometric mean can be taken. <br> | + | Then a geometric mean can be taken for a third number. <br> |
== In context of [[self-assembly]] == | == In context of [[self-assembly]] == | ||
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* [[System complexity scaling of self-assembly]] | * [[System complexity scaling of self-assembly]] | ||
* [[System complexity scaling of positional assembly]] | * [[System complexity scaling of positional assembly]] | ||
| + | ---- | ||
| + | * [[Technological percolation limit]] | ||
== Extermal links == | == Extermal links == | ||
* https://en.wikipedia.org/wiki/Polyomino – '''lattice animals''' | * https://en.wikipedia.org/wiki/Polyomino – '''lattice animals''' | ||
Latest revision as of 11:57, 16 November 2024
Rather than quantifying by size or atom count.
More sensible may be quantifying by the entropy instead.
I.e. quantifying by the logarithm of (an estimate of) the number of
all possible structure that can be encoded and actually built.
Calculating the exact number of accessible states can quickly become very difficult to impossible.
Upper and lower bound estimates beyond the most naive approaches can be accessible though.
Then a geometric mean can be taken for a third number.
Contents
In context of self-assembly
For a concrete example: 3D structural DNA nanotechnology
it is not that all voxel cominations are accessible
– there needs to be a contiguous connection between all of filled voxels
– connections need to be stiff enough for the structures to not deform too much
The former could be dealt with by known math for lattice animals (see links) if that where the only thing.
The latter complicates things further.
In context of positional assembly
Here beyond reachable size in terms of atom count
the limits of crystolecules and their systems may eventually be imposed by
minimal wall thicknesses and free standing structures (standoffs).
Related
Extermal links
- https://en.wikipedia.org/wiki/Polyomino – lattice animals
