English

The BiEntropy of Some Knots on the Simple Cubic Lattice

General Mathematics 2018-02-13 v1

Abstract

Binary representations of the trefoil and other knots of up to ten crossings in the simple cubic lattice were created. The BiEntropy of each knot was computed using a variety of binary encodings and compared against controls. This showed that binary encoded knots are highly disordered information objects. The BiEntropy of knots on the simple cubic lattice increases slightly as the number of crossings and length of encoding increases. We show that the non-alternating knots of nine and ten crossings are more disordered than the alternating knots of nine and ten crossings.

Keywords

Cite

@article{arxiv.1802.03772,
  title  = {The BiEntropy of Some Knots on the Simple Cubic Lattice},
  author = {Grenville J. Croll},
  journal= {arXiv preprint arXiv:1802.03772},
  year   = {2018}
}

Comments

11 Pages, 9 Colour Figures, 4 Tables; Originally presented at ANPA 36, Rowland's Castle, Hampshire, England, August 2016, with some minor revisions and clarifications