  In the literature, most of the results about the enumeration of directed
animals on lattices via gas considerations are obtained by a formal passage to
the limit of enumeration of directed animals on cyclical versions of the
lattice. Here we provide a new point of view on this phenomenon. Using the gas
construction given in [Electron. J. Combin. (2007) 14 R71], we describe the gas
process on the cyclical versions of the lattices as a cyclical Markov chain
(roughly speaking, Markov chains conditioned to come back to their starting
point). Then we introduce a notion of convergence of graphs, such that if
$(G_n)\to G$ then the gas process built on $G_n$ converges in distribution to
the gas process on $G$. That gives a general tool to show that gas processes
related to animals enumeration are often Markovian on lines extracted from
lattices. We provide examples and computations of new generating functions for
directed animals with various sources on the triangular lattice, on the
$\mathcal {T}_n$ lattices introduced in [Ann. Comb. 4 (2000) 269--284] and on a
generalization of the $\mathcaligr {L}_n$ lattices introduced in [J. Phys. A 29
(1996) 3357--3365].
