Self-assembly of homogeneous systems

The circle packings including non-periodic packings can be analysed for physical and thermodynamic stability for a triangular net with T(4) = 3-6 neighbours at distance d = root7; Two-dimensional structures A(x)B(y) are characterised by the numbers of T(4) neighbours and the ratio r=y/x of vacant/occupied positions of the triangular net. A small number of structures with maximum density p = 6.35/(r + 1) approach natural patterns of sunflower seeds, blackberries, bacteria, colloids, thistles or cactus spines. Two-dimensional patterns can be approached by combinations of the same structural units.