be found, and their relative statistical weight is controlled by persistence, as we show below. In order to give support to this claim, we run simulations on a rectangular surface( $L_x\times L_y$ with $L_x=5L_y$) with periodic boundary conditions. The choice of this geometry favors the formation of a macroscopic stripe along the short-axis $\mathbf{e}_y$, highlighting its band- or lane-like nature (see snapshots Fig. \[fig:Pxy\] and the movies in [@SM]).

![image](Pxy.pdf)

In order to identify systematically the band- or lane-like nature of the structure, we define, $P_x$ and $P_y$ as $$P_x = \left\langle \left |  \frac{1}{N} \sum_{i=1}^N\cos(\theta_i) \right | \right\rangle \, ; \, \, \,  \,  \,  \,  P_y = \left\langle  \left |  \frac{1}{N} \sum_{i=1}^N\sin(\theta_i) \right | \right\rangle\, ,$$ where $\left\langle.\right\rangle$ denotes an average over several independent configurations. These observables quantify the net polarization along the longitudinal and transverse direction in the slab geometry. We show in Fig. \[fig:Pxy\] the behavior of $P$, $P_{x}$ and $P_{y}$ as a function of the persistence of the system at fixed $\text{g}=10$. For $\text{Pe}\lesssim100$, the longitudinal order parameter is smaller than the transverse one, $P_x <P_y$, confirming that lanes prevail in the small $\text{Pe}$ regime (however, even in this regime, band and lane structures coexist, 