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Magnetic bright points in the solar photosphere, visible in both continuum and G-band images, indicate footpoints of kilogauss magnetic flux tubes extending to the corona. The power spectrum of bright-point motion is thus also the power spectrum of Alfvén wave excitation, transporting energy up flux tubes into the corona. This spectrum is a key input in coronal and heliospheric models. We produce a power spectrum of bright-point motion using radiative magnetohydrodynamic simulations, exploiting spatial resolution higher than can be obtained in present-day observations, while using automated tracking to produce large data quantities. We find slightly higher amounts of power at all frequencies compared to observation-based spectra, while confirming the spectrum shape of recent observations. This also provides a prediction for observations of bright points with DKIST, which will achieve similar resolution and high sensitivity. We also find a granule size distribution in support of an observed two-population distribution, and we present results from tracking passive tracers, which show a similar power spectrum to that of bright points. Finally, we introduce a simplified, laminar model of granulation, with which we explore the roles of turbulence and of the properties of the granulation pattern in determining bright-point motion. [ABSTRACT FROM AUTHOR]