  Active matter deals with systems whose particles consume energy at the
individual level in order to move. To unravel features such as the emergence of
collective structures several models have been suggested, such as the
on-lattice model of run-and-tumble particles implemented via the Persistent
Exclusion Process (PEP). In our work, we study a one dimensional system of
run-and-tumble repulsive or attractive particles, both on and off lattice.
Additionally, we implement a cluster motility dynamics in the on-lattice case
(since in the off-lattice case cluster motility arises from the individual
particle dynamics). While we observe important differences between discrete and
continuous dynamics, few common features are of particular importance.
Increasing particle density drives aggregation across all different systems
explored. For non-attractive particles, the effects of particle activity on
aggregation are largely independent of the details of the dynamics. On the
contrary, once attractive interactions are introduced, the steady state, which
is completely determined by the interplay between these and the particles'
activity, becomes highly dependent on the details of the dynamics.
