A genetic algorithm is used to search for the rhythmical control of eight joints in a quadruped robot. The search is used to find a fixed number of Fourier coefficients for each joint. Each set of coefficients is considered to be a controller for the robot, and it is evaluated using a simulator of the dynamics of the walking pattern generated by the controller. The fitness of a controller is higher if it generates more stable and faster walking. Effective controllers are further evaluated using a purpose-built robot that is physically modeled in the simulator. We present initial results from this simulation system, and show good correspondence between the simulator-generated dynamics and the movement of the robot under control of the same set of coefficients. The results presented here suggest that stable limit cycles may exist in the dynamics of quadruped walking.