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 oating car data to analyze and describe the movement characteristics of the minibus taxis in Kampala, Uganda. We made three intriguing ndings. Firstly, in searching for, picking up and transporting passengers, minibus taxi trajectories followed a heavy-tailed power-law distribution similar to a \L evy 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 signi cantly inecient. Our ndings 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. Keywords: Demand-responsive Transport, Taratransit, Minibus taxi, Matatu, Tortuosity, L evy walk, Self-organizing 1. Introduction In most African countries, minibus taxis are the backbone of public transportation. They transport more than 70% of the total urban travelers and dominate most social and economic aspects of urban mo- bility (Behrens et al., 2015). They form part of the broader organically evolved paratransit system that operates with little or no regulation in many developing cities of Africa and the Global South (Behrens et al., 2015). Minibus taxi transport is exible and semi-adaptive, with stops, schedules, fares and routes primar- ily determined by demand (Klopp and Cavoli, 2019). Unlike traditional bus rapid transit (BRT) systems that use buses on xed routes and schedules developed a long time in advance, minibus taxi drivers in a paratransit system often plan their routes according to the occupancy status of the taxi and anticipated demand (Gauthier and Weinstock, 2010). The rapid urban population growth (6% per annum) is reshaping urban settlements and changing eco- nomic and social population dynamics in Africa (Awumbila, 2017; Lucas et al., 2019). Coupled with weak and non-transit-oriented city development policies, the population surge in cities will increase the problems of urban sprawl, scattered public amenities and unemployment. The mobility characteristics of urban dwellers will consequently change, triggering a change in minibus taxi movement characteristics in response, and the static minibus taxi route maps proposed by Klopp and Cavoli (2019) will no longer be useful. By exploring the evolution of minibus taxi routes in Kampala's paratransit system, our study could pave the way for solutions to the future minibus taxi travel problems. Minibus taxis rarely get enough passengers to ll up before departure unless they start trips from the major taxi ranks (which are typically few and travelers often shun them). They therefore search for passengers on the way to make the trips pro table. Sometimes, they wait (\hold back") at selected stops in anticipation of passengers turning up, and sometimes, they go o the main route to search for passengers in sparsely distributed places where they anticipate demand for their services. The taxis go up and down the streets in an apparently chaotic fashion, hooting repeatedly, calling out their destinations, randomly inviting pedestrians to board the taxi, and stopping anywhere to tout for potential passengers in total disregard of trac and municipal laws. We suspected that analysis of these movements of minibus taxis would demonstrate a Preprint submitted to Journal of Transport Geography October 2, 2020 L evy walk pattern during the passenger search process (shown in Figure 1a). A \L evy walk" (a term we use synonymously with \L evy ight") is a pattern of movements made by a random walker, where many short movements are randomly interspersed with long ones and occasionally very long ones, as illustrated in Figure 1b(ii) (James et al., 2011). In Figure 1a, a minibus taxi moves from origin (O) to destination (D) but in the process makes many detours to hunt for passengers in o -route locations L, S, S0and L0. The L evy walk theory broadly combines an organisms' need for resources (e.g., food, shelter, or customers) and the need to reduce risks (e.g., from predators or competitors) with the density and renewability of resources to explain the organisms' movement in space. This study focuses on human movement where the minibus taxi driver represents the `random walker' and the minibus taxi travelers (trips demand) represent the resources being searched for under some predatory risks such as police enforcement, and competition from other minibus taxis on the same route. In our study we used oating car data (timestamped geo-localization data collected by moving vehicles) to characterize the movement patterns of minibus taxis in Kampala's organically evolved paratransit system. We were interested in discovering whether minibus taxi movement patterns were consistent with L evy walk behavior; whether the routes the taxis used changed topology or shape over time, in other words evolved; and whether their movements could suggest anything about their level of determination when searching for passengers. 2. The literature and applications to this study We divided the literature into three categories: the current status of paratransit in African cities, L evy walk behavior in animal and human movements, and spatial similarity analysis of mobility trajectories. 2.1. Current status of paratransit in African cities Until recently, the term \paratransit", meaning \beyond standard transit", or \alongside of standard transit", was used (mostly in the US), to refer to supplementary public transport services that do not have xed routes or timetables but instead respond to travel demand and p