  We study a simple geometric model for local transformations of bipartite
graphs. The state consists of a choice of a vector at each white vertex made in
such a way that the vectors neighboring each black vertex satisfy a linear
relation. Evolution for different choices of the graph coincides with many
notable dynamical systems including the pentagram map, $Q$-nets, and discrete
Darboux maps. On the other hand, for plabic graphs we prove unique
extendability of a configuration from the boundary to the interior, an elegant
illustration of the fact that Postnikov's boundary measurement map is
invertible. In all cases there is a cluster algebra operating in the
background, resolving the open question for $Q$-nets of whether such a
structure exists.
