  An automata network (AN) is a finite graph where each node holds a state from
a finite alphabet and is equipped with a local map defining the evolution of
the state of the node depending on its neighbors. The global dynamics of the
network is then induced by an update scheme describing which nodes are updated
at each time step. We study how update schemes can compensate the limitations
coming from symmetric local interactions. Our approach is based on intrinsic
simulations and universality and we study both dynamical and computational
complexity. By considering several families of concrete symmetric AN under
several different update schemes, we explore the edge of universality in this
two-dimensional landscape. On the way, we develop a proof technique based on an
operation of glueing of networks, which allows to produce complex orbits in
large networks from compatible pseudo-orbits in small networks.
