This document describes a tactile brush algorithm that uses apparent motion and phantom illusions to produce smooth, two-dimensional tactile strokes on the skin. The algorithm controls the frequency, intensity, velocity, and direction of tactile sensations produced by a low-resolution grid of vibrating actuators to create the illusion of high-resolution tactile motion. It utilizes apparent motion between actuators and phantom sensations from virtual actuators to generate continuous tactile motion that mimics physical brush strokes across the skin. The tactile brush algorithm provides an approach for designers to create complex, multidimensional tactile experiences using only basic tactile display hardware.