Information provided by sensory systems is inherently ambiguous as to its source in the physical world. To arrive at a coherent representation, perception deploys heuristic rules and multimodal input, which potentially produce errors such as illusions. The current work uses these effects to create apparent tactile motion and illusory depth motion using sparse vibrotactile stimulation across the hands. Experiment 1 showed the effects of vibrotactile duration and temporal separation between the hands on the quality of perceived illusory linear motion. Experiment 2 indicated a compressed linear relation between the visual and tactile speeds, and established a linear function relating visual size to perceived tactile intensity at three durations. Experiment 3 introduced an "M-filter" algorithm that varies tactile stimulus amplitude by a parabolic function based on visual looming and receding. It demonstrated that the M-filters, accompanied by visual depth cues, can induce tactile motion in depth. Experiment 4 showed the M-filter algorithm is necessary to create tactile perception in depth, as opposed to apparent tactile motion. The current research has value for a basic understanding of haptic perception, as well as haptic applications that digitally generate perceptual representations of the distal world on small-sized devices in the space between the hands.