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Stochastic porous structures are ubiquitous in natural phenomena and have gained considerable traction across diverse domains owing to their exceptional physical properties. The recent surge in interest in microstructures can be attributed to their impressive attributes, such as a high strength-to-weight ratio, isotropic elasticity, and bio-inspired design principles. Notwithstanding, extant stochastic structures are predominantly generated via procedural modeling techniques, which present notable difficulties in representing geometric microstructures with periodic boundaries, thereby leading to intricate simulations and computational overhead. In this manuscript, we introduce an innovative method for designing stochastic microstructures that guarantees the periodicity of each microstructure unit to facilitate homogenization. We conceptualize each pore and the interconnecting tunnel between proximate pores as Gaussian kernels and leverage a modified version of the minimum spanning tree technique to assure pore connectivity. We harness the dart-throwing strategy to stochastically produce pore locations, tailoring the distribution law to enforce boundary periodicity. We subsequently employ the level-set technique to extract the stochastic microstructures. Conclusively, we adopt Wang tile rules to amplify the stochasticity at the boundary of the microstructure unit, concurrently preserving periodicity constraints among units. Our methodology offers facile parametric control of the designed stochastic microstructures. Experimental outcomes on 3D models manifest the superior isotropy and energy absorption performance of the stochastic porous microstructures. We further corroborate the efficacy of our modeling strategy through simulations of mechanical properties and empirical experiments., Comment: 27 pages, 16 figures