Self-avoiding walk on a 15×15 square lattice wikipedia 
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. Very little is known rigorously about the self-avoiding walk from a mathematical perspective, although physicists have provided numerous conjectures that are believed to be true and are strongly supported by numerical simulations. wikipedia 
[…] SAWs and SAPs play a central role in the modeling of the topological and knot-theoretic behavior of thread- and loop-like molecules such as proteins.
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The enumeration of self-avoiding polygons is one of the most important and classical problems in enumerative combinatorics. –– Quantum Knots and Mosaics
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MADRAS, Neal Noah, MADRAS, Neal and SLADE, Gordon, 1996. The self-avoiding walk. Paperb. ed. Boston: Birkhäuser. Probability and its applications. ISBN 978-0-8176-3891-7.
See Biota.