  We use an information-theoretic measure of shape complexity known as
configurational entropy (CE) to investigate numerically the remarkably long
lifetimes of spherically-symmetric ``resonant oscillons'' in three-dimensional
and of azimuthally-symmetric oscillons in two-dimensional relativistic scalar
field theories, which have been conjectured to be infinite. In 3d, we obtain a
power law relating a stability measure derived from CE to the oscillons'
lifetimes that, upon extrapolation to large times, offers support to this
conjecture. In 2d, we obtain a three-way relation between the oscillons'
energies, a CE-derived measure of their stability, and their radiation rates to
support the conjecture that they asymptotically tend toward a
classically-stable attractor solution.
