# On the generation of periodic discrete structures with identical two-point correlation

arXiv: https://arxiv.org/abs/2002.01234 · HTML: https://mlsanity.com/paper/2002.01234/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Hybrid machine-learned homogenization: Bayesian data mining and convolutional neural networks](https://mlsanity.com/paper/2302.12545/) (2023)

## Abstract (arXiv)

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.