1009.2523 (Michael Damron et al.)

Examples of nonpolygonal limit shapes in i.i.d. first-passage
percolation and infinite coexistence in spatial growth models    [PDF]

Michael Damron, Michael Hochman

We construct an edge-weight distribution for i.i.d. first-passage percolation on $\mathbb{Z}^2$ whose limit shape is not a polygon and whose extreme points are arbitrarily dense in the boundary. Consequently, the associated Richardson-type growth model can support coexistence of a countably infinite number of distinct species, and the graph of infection has infinitely many ends.

View original: http://arxiv.org/abs/1009.2523