Animated mimic displays can be used to present system information regarding physical form, function, and causality. However, a potential limitation in current designs has been identified: the presence of ambiguous apparent motion. Two theoretical explanations of ambiguous apparent motion are discussed (Fourier and correspondence hypotheses). Two alternative designs (stair-step and approximate sinusoid luminance waveforms) were evaluated. The velocity matches obtained in Experiment 1 indicate that the sinusoidal waveform produced significantly better performance for both accuracy and latency than the stair-step wave-form. The velocity estimates obtained in Experiment 2 indicate that ambiguous apparent motion was not visible with the sinusoidal waveform, but was with the stair-step waveform. One of the two hypotheses (correspondence) provides a reasonable fit with the obtained velocity estimates. A fundamental goal in the design of animated mimic displays is to provide unambiguous mappings between perceived velocity and actual flow rates. Critical factors in design (e.g., waveform, chromatic/luminance contrast, spatial/temporal frequency) are discussed. Actual or potential applications of this research include the design of more effective animated mimic displays.