The functional significance of the zebra coat stripe pattern is one of the oldest questions in evolutionary biology, having troubled scientists ever since Charles Darwin and Alfred Russel Wallace first disagreed on the subject. While different theories have been put forward to address this question, the idea that the stripes act to confuse or 'dazzle' observers remains one of the most plausible. However, the specific mechanisms by which this may operate have not been investigated in detail. In this paper, we investigate how motion of the zebra's high contrast stripes creates visual effects that may act as a form of motion camouflage. We simulated a biologically motivated motion detection algorithm to analyse motion signals generated by different areas on a zebra's body during displacements of their retinal images. Our simulations demonstrate that the motion signals that these coat patterns generate could be a highly misleading source of information. We suggest that the observer's visual system is flooded with erroneous motion signals that correspond to two well-known visual illusions: (i) the wagon-wheel effect (perceived motion inversion due to spatiotemporal aliasing); and (ii) the barber-pole illusion (misperceived direction of motion due to the aperture effect), and predict that these two illusory effects act together to confuse biting insects approaching from the air, or possibly mammalian predators during the hunt, particularly when two or more zebras are observed moving together as a herd.