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Bertrand's theorem proves that inverse square and Hooke's law-type centralforces are the only ones for which all bounded orbits are closed. Similaranalysis was used to show that for other central force laws there exist closedorbits for a discrete set of angular momentum and energy values. These orbitscan in general be characterized as ``spirograph''-like, although specificorbits look more ``star''-like or ``triangular.'' We use the results of aperturbative version of Bertrand's theorem to predict which values of angularmomentum and energy result in closed orbits, and what their shapes will be.

Closed, spirograph-like orbits in power law central potentials