  This article introduces new tools to study self-organisation in a family of
simple cellular automata which contain some particle-like objects with good
collision properties (coalescence) in their time evolution. We draw an initial
configuration at random according to some initial $\sigma$-ergodic measure
$\mu$, and use the limit measure to descrbe the asymptotic behaviour of the
automata. We first take a qualitative approach, i.e. we obtain information on
the limit measure(s). We prove that only particles moving in one particular
direction can persist asymptotically. This provides some previously unknown
information on the limit measures of various deterministic and probabilistic
cellular automata: 3 and 4-cyclic cellular automata (introduced in [Fis90b]),
one-sided captive cellular automata (introduced in [The04]), N. Fat{\`e}s'
candidate to solve the density classification problem [Fat13], self
stabilization process toward a discrete line [RR15]... In a second time we
restrict our study to to a subclass, the gliders cellular automata. For this
class we show quantitative results, consisting in the asymptotic law of some
parameters: the entry times (generalising [KFD11]), the density of particles
and the rate of convergence to the limit measure.
