in angular size. The amplitude, phase and period of the variation are chosen randomly for each spot. We limit the period for spot size variation to lie between 5 and 20 times the rotation period. We generate light curves for each simulated star using the same time sampling as our observations. We then measure the period of each simulated light curve using the multi-harmonic AoV algorithm, rejecting light curves for which $N=1,2$ and $3$ do not return the same period within $10\%$. Figure \[fig:spotsimulation\] shows an example of a simulated light curve and the detected period as a function of the injected period for all simulations. We find the RMS difference between the injected and recovered periods is $\sim 5\%$. We also find that the $N=2$ period has the lowest RMS deviation from the injected rotation period. Note that this estimate for the error is conservative since most of the stars that we observed do not show as much spot evolution as our models do.

The rotation periods measured for an ensemble of stars with spots located at different latitudes may exhibit scatter even if all stars of a given mass have the same equatorial rotation period. The Sun exhibits 