A discrete-time model of, chemically or biologically, active fields advected by 
a 2D chaotic flow is studied. Our approach is based on the use of a lagrangian 
scheme where fluid particles are advected by a 2d symplectic 
map possibly yielding lagrangian chaos. Each fluid particle carries 
concentrations of active substances which evolve according to another map which 
mimics the reaction or population dynamics. Specifically, a logistic map is used 
where the bifurcation parameter is space dependent, simulating a spatially 
nonhomogenous distribution of nutrients or of activators. Exploiting the 
analogies of this coupled maps (advection plus reaction) system with a random 
map, some features of the different Eulerian 2d spatial patterns of the active 
particles concentration are discussed. In particular, we address the problem of 
the different patterns that appear depending on the behavior of the maps ruling 
the lagrangian and reactive dynamics.