  We consider a wide class of ergodic first passage percolation processes on
Z^2 and prove that there exist at least four one-sided geodesics a.s. We also
show that coexistence is possible with positive probability in a four color
Richardson's growth model. This improves earlier results of Haggstrom and
Pemantle, Garet and Marchand, and Hoffman who proved that first passage
percolation has at least two geodesics and that coexistence is possible in a
two color Richardson's growth model.
