The relative importance of nearest-neighbor and non-nearest-neighbor excursions of a dipolar species interacting with a fixed target molecule in the presence of a constellation of N fixed dipoles is explored. Particular attention is paid to the topology of the reaction space, and we contrast the results obtained for reactive processes confined to the d = 2 surface of a Cartesian shell vs. those obtained for a fractal solid, here the D = 2.7268 Menger sponge. The relevance of the results obtained to experimental studies on the lifetime of reactive species diffusing in/on the surface/interior of a zeolite is brought out. (C) 2002 Published by Elsevier Science B.V.