Active particles such as swimming bacteria or self-propelled colloids spontaneously self-organize into large-scale dynamic structures. The emergence of these collective states from the motility pattern of the individual particles, typically a random walk, is yet to be probed in a well-defined synthetic system. Here, we report the experimental realization of tunable colloidal motion that reproduces run-and-tumble and Lévy trajectories. We utilize the Quincke effect to achieve controlled sequences of repeated particle runs and random reorientations. We find that a population of these random walkers exhibit behaviors reminiscent of bacterial suspensions such as dynamic clusters and mesoscale turbulentlike flows.