Broad-band, photometric variability from accretion disks around black holes has been studied for the last five decades, yet it still is not understood. Given the large amount of data available on accreting stellar and supermassive black holes, in particular from numerous large, dedicated monitoring campaigns in different wavebands, plausible models exist to explain the variability from the accretion disks on different timescales that provide compelling explanations for the observed phenomenology. However, these models are largely based on the expected behavior of a viscous hydrodynamic accretion disk and have not been tested in the magnetohydrodyanmic (MHD) regime. We propose a series of studies to test the various physical processes expected to give rise to the complex variability seen from accreting black holes using large viscous hydrodynamic and MHD simulations of canonical thin accretion disks. We will analyze these simulations looking “ through the lens of the observer” in order to elucidate the processes driving variability by connecting the observed signatures with the detailed, underlying physics. In particular, we will focus on understanding the role thermal instabilities play in driving intermediate timescale variability and how large-scale magnetic field is generated through dynamo processes and is removed. The results from our work will resolve debates in the literature regarding the previously observed variable behavior of accreting stellar and supermassive black hole systems, for instance by the long monitoring campaigns conducted by NASA's Swift and Kepler missions. Additionally, this work will lay the theoretical ground-work for the analysis of variability observed by future monitoring campaigns of black holes like those that will be conducted serendipitously in the search for transiting exoplanets by NASA's upcoming TESS mission.