Fig. 4 | Nature Communications

Fig. 4

From: Universal hidden order in amorphous cellular geometries

Fig. 4

Effectively hyperuniform and universal final configurations in 2D with local crystallites. Frequency distribution f(e) of cell energy densities e (see Methods section) are shown before (a) and after (b) application of 104 iterations of Lloyd’s algorithm (see Methods section for initial point processes). The error bars represent the standard error of the mean. In the final configurations, which are effectively universal, only a small portion of cells (0.2%) has an energy density lower than that of the (globally optimal) regular hexagon. Here esq is the energy density of the square lattice. c Voronoi cells in the final CVT: The colour code indicates the difference between the isoperimetric ratio Q = 4πA/P2 of each cell, where A is the area and P the perimeter of the cell, and the isoperimetric ratio Qhex = 0.9069 of the regular hexagon. The local crystallites and their globally amorphous arrangement are clearly visible. For the structure factor of the initial and final configurations, see Supplementary Fig. 4

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