Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation

Edward Bormashenko; Irina Legchenkova; Mark Frenkel

doi:10.3390/e21050452

Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation

Entropy (Basel). 2019 Apr 30;21(5):452. doi: 10.3390/e21050452.

Authors

Edward Bormashenko¹, Irina Legchenkova¹, Mark Frenkel¹

Affiliation

¹ Department of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel.

Abstract

The Voronoi entropy for random patterns and patterns demonstrating various elements of symmetry was calculated. The symmetric patterns were characterized by the values of the Voronoi entropy being 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. Extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables the elements of symmetry of the patterns to be revealed.

Keywords: Shannon measure of information; Voronoi entropy; Voronoi tessellation; ordering; symmetry.