Any path—periodic or not, closed or open—can be represented with an infinite number of epicycles. This is because epicycles can be represented as a complex Fourier series; therefore, with a large number of epicycles, very complex paths can be represented in the complex plane.See, e.g., this animation made by Christián Carman and Ramiro Serra, which uses 1000 epicycles to retrace the cartoon character Homer Simpson; see also Christián Carman's "Deferentes, epiciclos y adaptaciones." and "La refutabilidad del Sistema de Epiciclos y Deferentes de Ptolomeo".
