  In this paper, we study the clustering of inertial particles using a periodic
kinematic simulation. The systematic Lagrangian tracking of particles makes it
possible to identify the particles' clustering patterns for different values of
particle inertia and drift velocity. The different cases are characterised by
different pairs of Stokes number $St$ and Froude number $Fr$. For the present
study $0\leq St \leq 1$ and {$0.4 \leq Fr \leq 1.4$}. The main focus is to
identify and then quantify the clustering attractor - when it exists - that is
the set of points in the physical space where the particles settle when time
goes to infinity. Depending on gravity effect and inertia values, the
Lagrangian attractor can have different dimensions varying from the initial
three-dimensional space to two-dimensional layers and one-dimensional
attractors that can be shifted from a horizontal to a vertical position.
