Dynamic localization, which originates from the phenomena of particle evolution suppression under an externally applied AC electric field, has been simulated by suppressed light evolution in periodically curved photonic arrays. However, experimental studies on their quantitative dynamic transport properties and application for quantum information processing are rare. Here we fabricate one-dimensional and hexagonal two-dimensional arrays both with sinusoidal curvatures. We successfully observe the suppressed single-photon evolution patterns, and for the first time, to the best of our knowledge, measure the variances to study their transport properties. For one-dimensional arrays, the measured variances match both the analytical electric-field calculation and the quantum walk Hamiltonian engineering approach. For hexagonal arrays as anisotropic effective couplings in four directions are mutually dependent, the analytical approach suffers, whereas quantum walk conveniently incorporates all anisotropic coupling coefficients in the Hamiltonian and solves its exponential as a whole, yielding consistent variances with our experimental results. Furthermore, we implement a nearly complete localization to show that it can preserve both the initial injection and the wave packet after some evolution, acting as a memory of a flexible time scale in integrated photonics. We demonstrate a useful quantum simulation of dynamic localization for studying their anisotropic transport properties and a promising application of dynamic localization as a building block for quantum information processing in integrated photonics.