A gyricon or rotating-particle display having an "eggcrate" substrate. The display includes a substrate having a cavity-containing matrix whose cavities are disposed substantially in a single layer and are arranged within the matrix substantially in a geometrically regular pattern, and a plurality of optically anisotropic particles disposed in the cavities in the substrate, with each cavity containing at most one of the optically anistropic particles. A rotatable disposition of each particle is achievable while the particle is thus disposed in the substrate; the particle, when in its rotatable disposition, is not attached to the substrate. Each particle, for example, can have an anisotropy for providing an electrical dipole moment, the electrical dipole moment rendering the particle electrically responsive such that when the particle is rotatably disposed in an electric field while the electrical dipole moment of the particle is provided, the particle tends to rotate to an orientation in which the electrical dipole moment aligns with the field. The single layer of cavities can be substantially planar, and the geometrical pattern of cavities can be a two-dimensional array pattern in the plane of the layer, such as a hexagonal, rectangular, or rhomboidal array pattern. The substrate can further include first and second members between which members the matrix is disposed; at least one of the members can include an optically transmissive window through which a flux of optical energy can pass so as to be incident on the particles.