A double Pulsed Gradient Spin Echo (d-PGSE) MR experiment was used to measure and assess the degree of local diffusion anisotropy in brain gray matter, and in a novel "gray matter" phantom that consists of randomly oriented tubes filled with water. In both samples, isotropic diffusion was observed at a macroscopic scale while anisotropic diffusion was observed at a microscopic scale, however, the nature of the resulting echo attenuation profiles were qualitatively different. Gray matter, which contains multiple cell types and fibers, exhibits a more complicated echo attenuation profile than the phantom. Since microscopic anisotropy was observed in both samples in the low q regime comparable to that achievable in clinical scanner, it may offer a new potential contrast mechanism for characterizing gray matter microstructure in medical and biological applications.