  Strategies for the generation of periodic discrete structures with identical
two-point correlation are developed. Starting from a pair of root structures,
which are not related by translation, phase inversion or axis reflections,
child structures of arbitrary resolution (i.e., pixel or voxel numbers) and
number of phases (i.e., material phases/species) can be generated by means of
trivial embedding based phase extension, application of kernels and/or phase
coalescence, such that the generated structures inherit the
two-point-correlation equivalence. Proofs of the inheritance property are
provided by means of the Discrete Fourier Transform theory. A Python 3
implementation of the results is offered by the authors through the Github
repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make
the provided results reproducible and useful for all interested readers.
Examples for the generation of structures are demonstrated, together with
applications in the homogenization theory of periodic media.
