Self-avoiding walk of 33554431 steps on the simple cubic lattice by Nathan Clisby

This is a self-avoiding walk sampled from the uniform distribution 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 3d 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.