Bormashenko, E.; Legchenkova, I.; Frenkel, M. Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation. Entropy 2019, 21, 452, doi:10.3390/e21050452.
Bormashenko, E.; Legchenkova, I.; Frenkel, M. Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation. Entropy 2019, 21, 452, doi:10.3390/e21050452.
Bormashenko, E.; Legchenkova, I.; Frenkel, M. Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation. Entropy 2019, 21, 452, doi:10.3390/e21050452.
Bormashenko, E.; Legchenkova, I.; Frenkel, M. Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation. Entropy 2019, 21, 452, doi:10.3390/e21050452.
Abstract
Voronoi entropy for the random patterns and patterns demonstrating various elements of symmetry are calculated. The symmetric patterns are characterized by the values of the Voronoi entropy very close to those inherent to random ones. This contradicts the idea that the Voronoi entropy quantifies the ordering of the seed points, constituting the pattern. The extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables revealing of the elements of symmetry of the pattern.
Keywords
Voronoi entropy; Voronoi tessellation; symmetry; ordering; Shannon measure of information
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
