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The Galactic disk is expected to be spatially, kinematically, and chemically clustered on many scales due to both star formation and non-axisymmetries in the Galactic potential. In this work we calculate the spatial and kinematic two-point correlation functions using a sample of $1.7 \times 10^6$ stars within 1 kpc of the Sun with 6D phase space information available from \textit{Gaia} DR2. Clustering is detected on spatial scales of 1-300 pc and velocity scales of at least 15 km s$^{-1}$. With bound structures included, the data have a power-law index ($ξ(Δr) \propto Δr^γ$) of $γ\approx-2$ at most spatial scales, which is in line with theoretical predictions. After removing bound structures, the data have a power-law index of $γ\approx-1$ for $<100$ pc and $γ\lesssim -1.5$ for $>100$ pc. We interpret these results with the aid of a novel star-by-star simulation of the Galaxy in which stars are born in clusters orbiting in a realistic potential that includes spiral arms, a bar, and GMCs. We find that the simulation largely agrees with the observations (within a factor of 2-3) at all spatial and kinematic scales. In detail, the correlation function in the simulation is shallower than the data at $< 20$ pc scales, and steeper than the data at $> 30$ pc scales. We also find a persistent clustering signal in the kinematic correlation function for the data at large $Δv$ ($>5$ km s$^{-1}$) not present in the simulations. We speculate that this mismatch between observations and simulations may be due to two processes not included in the simulation: hierarchical star formation and transient spiral arms. We also use the simulations to predict the clustering signal as a function of pair-wise metallicity and age separations. Ages and metallicities measured with a precision of $50\%$ and $0.05$ dex are required in order to enhance the clustering signal.