  Changing a circuit dynamically, without actually changing the hardware
itself, is called reconfiguration, and is of great importance due to its
manifold technological applications. Circuit reconfiguration appears to be a
feature of the cerebral cortex, and hence understanding the neuroarchitectural
and dynamical features underlying self-reconfiguration may prove key to
elucidate brain function. We present a very simple single-layer recurrent
network, whose signal pathways can be reconfigured "on the fly" using only its
inputs, with no changes to its synaptic weights. We use the low spatio-temporal
frequencies of the input to landscape the ongoing activity, which in turn
permits or denies the propagation of traveling waves. This mechanism uses the
inherent properties of dynamically-critical systems, which we guarantee through
unitary convolution kernels. We show this network solves the classical
connectedness problem, by allowing signal propagation only along the regions to
be evaluated for connectedness and forbidding it elsewhere.
