3 \left( \frac{\sigma}{r_{c}}
\right)^{6} \right] \left( \frac{r_{ij}}{r_{c}}
\right)^{2}
 - 4\epsilon \left[ 7 \left(\frac{\sigma}{r_{c}}
\right)^{12} + 4 \left( \frac{\sigma}{r_{c}}
\right)^{6} \right]\,,   \end{aligned}$$

whereas for $r_{ij} < (2.2^{1/6}\sigma)$ $V_{att}=-0.305 \epsilon$ and $V_{att}=0$ otherwise.

Inspired by the work of Hong [*et al.*]{} [@langmuir08] for amphiphilic colloidal spheres, the anisotropic interaction is controlled by the angular contribution of the attractive potential $$\begin{aligned}
\label{eq:phi}
\begin{split}
&\phi(\theta_i,\theta_j)=&\\
&\begin{cases}
\cos\theta_i \cos \theta_j &\left( \hat{p}_i \cdot \hat{\mu}_{ji} \right) > 0 \cap \left( \hat{p}_j \cdot \hat{\mu}_{ij} \right) > 0\,,\\
0 & otherwise\,.\\
\end{cases}
\end{split}\end{aligned}$$ where $\hat{\mu}_{ij} = \vec{r}_{ij}/r_{ij}$ is the unit vector joining the squirmers’ center of mass. This anisotropic potential ensures a non-vanishing torque when $\left( \hat{p}_i \cdot \hat{\mu}_{ji} \right) > 0 $ and $ \left( \hat{p}_j \cdot \hat{\mu}_{ij} \right) > 0$ (a more detailed analysis is discussed in appendix \[Appendix:JanusOrient\]).

Within our model, each Janus particle self-propels along a direction $\hat{e}_i$ rigidly bounded to the particle. As in Ref. [@Stewart_17], we study two types of active Janus particles depending of the orientation of $\hat{e}_i$ with respect to $\hat{p}_i$. When the propulsion direction ($\hat{e}_i$, red arrow in figure \[fig:JanusSquirmers\]-left panel) is pointing towards the attractive patch $\hat{p}_i$ (red arrow in figure \[fig:JanusSquirmers\]-left panel), swimmers are propelling “with the 