Frenkel, M.; Legchenkova, I.; Shvalb, N.; Shoval, S.; Bormashenko, E. Voronoi Diagrams Generated by the Archimedes Spiral:Fibonacci Numbers, Chirality and Aesthetic Appeal. Symmetry2023, 15, 746.
Frenkel, M.; Legchenkova, I.; Shvalb, N.; Shoval, S.; Bormashenko, E. Voronoi Diagrams Generated by the Archimedes Spiral:Fibonacci Numbers, Chirality and Aesthetic Appeal. Symmetry 2023, 15, 746.
Frenkel, M.; Legchenkova, I.; Shvalb, N.; Shoval, S.; Bormashenko, E. Voronoi Diagrams Generated by the Archimedes Spiral:Fibonacci Numbers, Chirality and Aesthetic Appeal. Symmetry2023, 15, 746.
Frenkel, M.; Legchenkova, I.; Shvalb, N.; Shoval, S.; Bormashenko, E. Voronoi Diagrams Generated by the Archimedes Spiral:Fibonacci Numbers, Chirality and Aesthetic Appeal. Symmetry 2023, 15, 746.
Abstract
Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from a sells of equal size which are of a primary importance for decorative arts are reported. The pronounced prevalence of hexagons is inherent for the patterns with an equidistant and non-equidistant distribution of points, when the distance between the seed points is of the same order of magnitude as the distance between the turns of the spiral. Penta- and heptagonal “defected” cells appeared in the Voronoi diagrams due to the finite nature of the pattern. The ordered Voronoi tessellations demonstrating the Voronoi entropy larger than 1.71, reported for the random 2D distribution of points, were revealed. The dependence of the Voronoi entropy on the total number of the seed points located on the Archimedes Spirals is reported. Voronoi tessellations generated by the phyllotaxis-inspired patterns are addressed. The aesthetic attraction of the Voronoi mosaics arising from seed points placed on the Archimedes Spirals is discussed.
Keywords
Archimedes Spiral; Voronoi tessellation; Voronoi entropy; surface patterns; aesthetic attraction; phyllotaxis; golden ratio
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.
