Symmetric patterns of dislocations in Thomson’s problem

1999 ◽  
Vol 60 (23) ◽  
pp. 15628-15631 ◽  
Author(s):  
A. Pérez-Garrido ◽  
M. A. Moore
Keyword(s):  
Symmetric Patterns

scholarly journals Phyllotaxis as geometric canalization during plant development

Development ◽  
2020 ◽  
Vol 147 (19) ◽  
pp. dev165878 ◽  
Author(s):  
Christophe Godin ◽  
Christophe Golé ◽  
Stéphane Douady
Keyword(s):  
Developmental Biology ◽  
Plant Development ◽  
Fundamental Question ◽  
Developmental Constraints ◽  
Local Interactions ◽  
Final Shape ◽  
Lateral Organs ◽  
Universal Constraint ◽  
Symmetric Patterns

ABSTRACTWhy living forms develop in a relatively robust manner, despite various sources of internal or external variability, is a fundamental question in developmental biology. Part of the answer relies on the notion of developmental constraints: at any stage of ontogenesis, morphogenetic processes are constrained to operate within the context of the current organism being built. One such universal constraint is the shape of the organism itself, which progressively channels the development of the organism toward its final shape. Here, we illustrate this notion with plants, where strikingly symmetric patterns (phyllotaxis) are formed by lateral organs. This Hypothesis article aims first to provide an accessible overview of phyllotaxis, and second to argue that the spiral patterns in plants are progressively canalized from local interactions of nascent organs. The relative uniformity of the organogenesis process across all plants then explains the prevalence of certain patterns in plants, i.e. Fibonacci phyllotaxis.

An Improved Microphotometer Trace of Radially Symmetric Patterns

1947 ◽  
Vol 15 (10) ◽  
pp. 765-765 ◽  
Author(s):  
I. Lugoski Karle ◽  
D. Hoober ◽  
J. Karle
Keyword(s):  
Symmetric Patterns

X-ray reflection from thin multilayers: symmetric patterns

2003 ◽  
Vol 35 (1) ◽  
pp. 76-79 ◽  
Author(s):  
Pavel Karimov ◽  
Shingo Harada ◽  
Jun Kawai
Keyword(s):  
X Ray ◽  
Symmetric Patterns

scholarly journals Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation

2019 ◽  
Author(s):  
Edward Bormashenko ◽  
Irina Legchenkova ◽  
Mark Frenkel
Keyword(s):  
Voronoi Tessellation ◽  
Voronoi Diagrams ◽  
Random Patterns ◽  
Seed Points ◽  
Symmetric Patterns

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.

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