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For most large quadrupedal mammals, galloping is the preferred gait for high-speed locomotion. In this paper we evolve a gallop gait in a simulated quadruped robot at speeds from 3.0 to 10.0 m/s. To do so, we must generate periodic trajectories for the body and legs. An evolutionary algorithm known as set-based stochastic optimization (SBSO) is used to find the body trajectory while alternative methods are used to find periodic leg trajectories. The focus of this paper will be to evaluate three different methods for generating periodic leg trajectories. The combined solutions for the body and legs yield biological characteristics that are emergent properties of the underlying high-speed dynamic running gait.