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Self-avoiding walk of 33554431 steps on the 4d hypercubic lattice, projection #1 by Nathan Clisby

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About This Gigapan

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Taken by
Nathan Clisby Nathan Clisby
Explore score
1
Size
0.08 Gigapixels
Views
251
Date added
Jun 01, 2012
Date taken
 
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Description

This self-avoiding walk was generated via a new implementation of the pivot algorithm.

The self-avoiding walk (SAW) is an extremely simple model: a SAW is a walk on the lattice such that no lattice vertex is visited twice. However, it exactly captures the essential physics of the behaviour of polymers in a good solvent, e.g. the Flory exponent (nu) is exactly the same for SAW as it is for real polymers.

This image is a simple projection of the 4d object, with no information about depth. Note that the reason that is more dense than a 2d SAW because the extra dimension gives the walk more freedom, and the walk doesn't repel itself as strongly.

In fact, this projection of a 4d walk should almost look like pure Brownian motion, as nu=0.5 with logarithmic corrections.


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