  A beta-skeleton is a planar proximity undirected graph of an Euclidean point
set where nodes are connected by an edge if their lune-based neighborhood
contains no other points of the given set. Parameter $\beta$ determines size
and shape of the nodes' neighborhoods. In an excitable beta-skeleton every node
takes three states --- resting, excited and refractory, and updates its state
in discrete time depending on states of its neighbors. We design families of
beta-skeletons with absolute and relative thresholds of excitability and
demonstrate that several distinct classes of space-time excitation dynamics can
be selected using beta. The classes include spiral and target waves of
excitation, branching domains of excitation and oscillating localizations.
