The photometric behavior of Sun-like stars -- from long-timescale variations attributed to the rotational

modulation of spots to high-frequency acoustic oscillations -- changes as stars spin down on the main-

sequence and then as they evolve to become subgiants and red giants. Using Kepler long-cadence light

curves, we present a unified picture of how the photometric behavior of Sun-like stars on hours to days

timescales evolves with time. We find that stars exhibit clear evolutionary sequences in diagrams of

three simple photometric variability measures, thereby providing a "fundamental plane" of

evolution akin to the Hertzsprung-Russell diagram, but involving only simple measures of photometric

variability. We observe that the light curves of these stars become "quieter" as the stellar spot coverage

decreases with time, but that they become suddenly and significantly more complex as stars approach

their evolution off the main-sequence and spots no longer dominate the brightness variations. Using an

asteroseismically analyzed sample of stars, we demonstrate that the sequences in our diagram are a

strong function of stellar surface gravity, yielding a simple tool to accurately measure this quantity to

better than 25% with just the long-cadence light curve. The Sun also obeys these newly found

relationships: we correctly recover its surface gravity to within 25% with just our simple measures of

photometric variability. We suggest that the brightness variations we observe trace granulation,

manifesting in a remarkably simpler fashion than previously appreciated, and we show how these

stellar brightness variations can be used to enhance extrasolar planet detection and characterization.