Construction of digital realizations of anisotropic hyperuniform continuous random fields in two and three dimensions via generalized spectral filtering

Hyperuniform continuous random fields suppress large-scale fluctuations while preserving rich local disorder, making them highly attractive for next-generation photonic, thermal, and mechanical materials. However, traditional construction techniques rendering digital realizations of the random fields often suffer from limited spectral control or excessive computational cost, especially in high-resolution two- and three-dimensional settings. In this work we present a generative algorithm based on generalized superellipse spectral filtering, which allows independent tuning of isotropic and anisotropic spectral envelopes without resorting to costly iterative schemes. We demonstrate our method on a comprehensive set of two- and three-dimensional examples, showing precise manipulation of spectral band shape and speedup of orders of magnitude compared to existing approaches. Furthermore, we examine simple sign thresholding of the continuous fields and report the resulting ±1 two-phase maps, which inherit shell-shaped spectral motifs while generally not preserving exact hyperuniformity. This work opens new avenues for large-scale simulation and optimized design of advanced hyperuniform materials.