  A stochastic partial differential equation along the lines of the
Kardar-Parisi-Zhang equation is introduced for the evolution of a growing
interface in a radial geometry. Regular polygon solutions as well as radially
symmetric solutions are identified in the deterministic limit. The polygon
solutions, of relevance to on-lattice Eden growth from a seed in the zero-noise
limit, are unstable in the continuum in favour of the symmetric solutions. The
asymptotic surface width scaling for stochastic radial interface growth is
investigated through numerical simulations and found to be characterized by the
same scaling exponent as that for stochastic growth on a substrate.
