Preprint Article Version 1 This version is not peer-reviewed

Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation

Version 1 : Received: 28 April 2019 / Approved: 30 April 2019 / Online: 30 April 2019 (11:51:44 CEST)

How to cite: Bormashenko, E.; Legchenkova, I.; Frenkel, M. Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation. Preprints 2019, 2019040336 (doi: 10.20944/preprints201904.0336.v1). Bormashenko, E.; Legchenkova, I.; Frenkel, M. Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation. Preprints 2019, 2019040336 (doi: 10.20944/preprints201904.0336.v1).

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.

Subject Areas

Voronoi entropy; Voronoi tessellation; symmetry; ordering; Shannon measure of information

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