View source for Quantifying progress by scaling in achievable complexity

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Rather than quantifying by size or atom count. <br>
More sensible may be quantifying by the entropy instead. <br>
Logarithm of (an estimate of) the number all possible structure that can be encoded and actually built. <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>
Then a geometric mean can be taken. <br>

== In context of  [[self-assembly]] ==

For a concrete example: 3D [[structural DNA nanotechnology]] <br>
it is not that all voxel cominations are accessible <br>
– there needs to be a contiguous connection between all of filled voxels <br>
– connections need to be stiff enough for the structures to not deform too much <br>
The former could be dealt with by known math for lattice animals (see links) if that where the only thing. <br>
The latter complicates things further. <br>

== In context of [[positional assembly]] ==

Here beyond reachable size in terms of atom count <br>
the limits of [[crystolecules]] and their systems may eventually be imposed by <br>
minimal wall thicknesses and free standing structures (standoffs). <br>

== Related ==

* [[System complexity scaling of self-assembly]]
* [[System complexity scaling of positional assembly]]

== Extermal links ==

* https://en.wikipedia.org/wiki/Polyomino – '''lattice animals'''