As a particle undergoes translational Brownian motion in an unbounded space, the particle samples the space. Traditionally the sampling in N dimensions is quantified in terms of average squared distance traversed ((x (.) x)). However, another quantitative measure of the sampled space is the total number (n) of equispaced regions (of size L-N) sampled after a particle moves with a diffusion coefficient (D) for a time (t). Calculations show that the average (n) = a(Dt/L-2)(b). Results are given for a and b for 1, 2, 3, and 4 dimensions. (C) 2004 Elsevier Inc. All rights reserved.