Urban travelers in Africa depend on minibus taxis for their daily social and business commuting. This paratransit system is loosely regulated, self-organizing, and evolves organically in response to demand. Our study used floating car data to analyze and describe the movement characteristics of the minibus taxis in Kampala, Uganda. We made three intriguing findings. Firstly, in searching for, picking up and transporting passengers, minibus taxi trajectories followed a heavy-tailed power-law distribution similar to a "Lévy walk". Secondly, their routes gradually evolved. Thirdly, the extraordinary winding (expressed in terms of tortuosity) of the paths suggested the extreme determination of the drivers' search for passengers. Overall, we found that the passenger search strategies used by the taxis were significantly inefficient. Our findings could help city planners to build on the self-organizing characteristics of the minibus taxi system, and improve the mobility of travelers, by optimizing routes and the distribution of public amenities.