Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation.

Edward Bormashenko, Irina Legchenkova, Mark Frenkel

Abstract read

In one paragraph

Article in Entropy (Basel, Switzerland), 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.

0numbers the graph read from it

0cells of the map it votes in

2citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

2 citing papers in PubMed.

The Role of Information Entropy in Symmetry of Euclidean Polygons.Entropy (Basel, Switzerland) · 2026
Article
Entropy, Information, and Symmetry: Ordered is Symmetrical.Entropy (Basel, Switzerland) · 2019
Article

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

3 authors.

Edward BormashenkoDepartment of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel.ORCID 0000-0003-1356-2486

Irina LegchenkovaDepartment of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel.

Mark FrenkelDepartment of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel.

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

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.

Indexed as

orderingShannon measure of informationsymmetryVoronoi entropyVoronoi tessellation

Identifiers

PMID33267166

DOI10.3390/e21050452

PMCPMC7514941

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.