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Mote3D is an adaptable, easy-to-use open-source software toolbox for the generation of random particulate microstructure models with periodic boundaries. Mote3D can be used to generate virtual models that represent the microstructure of various inhomogeneous engineering materials such as particle-reinforced composites, partially sintered ceramics, powders, open-cell foams or concrete aggregates, as well as of certain biomaterials or scaffolds.