13 0.5 1 0 0.1 P( 0 0.4 0.8 P$^{2}$ = [P$_{x}$$^{2}$ + P$_{y}$$^{2}$] 0 0.04 0.08 P(P 2 ) $_{0}$ = 0.6 $_{0}$ = 0.7 $_{0}$ = 0.8 0.5 1 0 0.1 0.2 P( v$_{0}$ = 0.1 v$_{0}$ = 0.3 v$_{0}$ = 0.5 v$_{0}$ = 0.7 0 0.4 0.8 0 0.1 P(P 2 ) v$_{0}$ = 0.1 v$_{0}$ = 0.3 v$_{0}$ = 0.5 v$_{0}$ = 0.7 (a) (b) (c) (d) FIG. 9: (color online) (a)-(c) Density and (b)-(d) order parameter histograms. In panels (a) and (b) the histograms are shown for ρ 0 = 0 . 7, v 0 = 0 . 1, 0 . 3, 0 . 5, 0 . 7 and L = 128. For small v 0 , below the threshold value v$_{c}$ ≃ 0 . 42, the histograms are unimodal (fitted by a Gaussian), indicating a uniform state. For v 0 > v$_{c}$ , the histograms are bimodal (fitted by two Gaussian curves), indicating the onset of stripes. In panels (c) and (d) the histograms are shown for v 0 > v$_{c}$ and three values of the mean density, ρ 0 = 0 . 6, 0 . 7, 0 . 8. The position of the peaks does not change with density, while the difference in the height of the two peaks increases with increasing density. Eqs. (30) and (31) that there is no propagating front so- lution if we turn off the couplings between density and polarization. solution represents a propagating domain boundary of effective thickness Λ between a state with P = 1 and a state with P = 0. In physical units, the length scale controlling the crossover between isotropic and polarized states, hence the sharpness of the stripes, is given by (3 πv$_{0}$/ℓD$_{r}$ ). This length is essentially the distance trav- eled by a self propelled particle in a rotational diffusion time. In other words, stripe formation is controlled by the formation of domain boundaries in the polarization, and the fact that the density is slaved to the polarization and hence leads to mass fluxes that delineate the two re- gions in the striped phase. Finally, it is apparent from In this work we have considered a continuum descrip- tion of a collection of self propelled particles moving in a passive medium. Their dynamics on large length and time scales is governed by hydrodynamic equations for the density and the polarization field. The crucial physics V. SUMMARY