Morphometry and structure of natural random tilings

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 33; no. 4; pp. 369 - 375
• Main Authors: Hočevar, A., El Shawish, S., Ziherl, P.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-12-2010; EDP Sciences
• Subjects: Animals; Biological and Medical Physics; Biological and medical sciences; Biophysics; Cell Shape; Complex Fluids and Microfluidics; Complex Systems; Drosophila - classification; Drosophila - cytology; Drosophila - physiology; Epithelial Cells - classification; Epithelial Cells - cytology; Epithelial Cells - physiology; Fundamental and applied biological sciences. Psychology; General aspects; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Models, Biological; Nanotechnology; Physics; Physics and Astronomy; Polymer Sciences; Regular Article; Soft and Granular Matter; Surfaces and Interfaces; Thin Films; Experimental Tiling; Voronoi Tesselations; Bivariate Distribution; Model Tiling; Polygon Area; Tissue; Two dimensional space; Plant origin; Animal origin; Tiling; Mathematical model; Morphometry; Polygon; Cell
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/i2010-10676-1

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A vast range of both living and inanimate planar cellular partitions obeys universal empirical laws describing their structure. To better understand this observation, we analyze the morphometric parameters of a sizeable set of experimental data that includes animal and plant tissues, patterns in desiccated starch slurry, suprafroth in type-I superconductors, soap froths, and geological formations. We characterize the tilings by the distributions of polygon reduced area, a scale-free measure of the roundedness of polygons. These distributions are fairly sharp and seem to belong to the same family. We show that the experimental tilings can be mapped onto the model tilings of equal-area, equal-perimeter polygons obtained by numerical simulations. This suggests that the random two-dimensional patterns can be parametrized by their median reduced area alone.