  Flow through passive porous media is typically described in terms of a linear
theory relating current fluxes and driving forces, in the presence of a
prescribed heterogeneous permeability. However, many porous systems such as
glacial drainage networks, erosional river bed networks, vascular networks,
social insect swarms and animal architectures such as termite mounds are
continuously remodeled by the flow and thence modify the flow, i.e. they are
active. Here we consider a minimal model for an active porous medium where flow
and resistance are coupled to each other. Using numerical simulations, we show
that this results in both channelization and wall-building transitions
depending on the form of the feedback. A continuum model allows us to
understand the qualitative features of the resulting phase diagram, and
suggests ways to realize complex architectures using simple rules in engineered
systems.
