Growth of random plane graphs and packings
Владимир Георгиевич Журавлев, Andrey V. Maleev, V. Guruprasada Rau, Антон Владимирович Шутов · Crystallography Reports · 2002
The process of growth of random graphs with the vertices lying at the points of the plane ( i, j ) with integral coordinates has been considered. Computer simulation of the process allowed us to establish that random graphs grow in the self-similar mode. The sectorial growth proceeds in such a way that the growth boundary in four sectors consists of two horizontal and two vertical linear segments; in the other four sectors, the boundary is a part of an ellipse; the real growth boundary lags behind the limited form to which it tends; the scatter interval along the principal growth diagonal is proportional to the cubic root of the number of the coordination sphere.