Morphology-induced Dispersion Anisotropy in Self-organized Phononic Media Derived from Reaction-diffusion Patterns

In this study, the morphology-induced dispersion anisotropy is examined in self-organized phononic media generated from reaction-diffusion (RD) patterns. Two-dimensional patterns are produced using the Gray-Scott model, and their characteristic wavelength and directional features are quantified by spatial Fourier analysis. These patterns are mapped onto spatially varying material-property fields, and wave-dispersion characteristics are computed using a scalar plane wave expansion method. Rather than focusing solely on complete bandgap formation, the manner in which characteristic length scales and morphological anisotropy influence band dispersion, equal-frequency contours, and group-velocity directionality is examined herein. Results show that RD patterns induce pronounced anisotropic dispersion even without a complete bandgap. The temporal evolution of morphology leads to systematic changes in interface density, dominant wavelength, and spectral anisotropy, accompanied by stage-dependent variations in low-order dispersion branches. Although the global linear correlation between morphology anisotropy and dispersion anisotropy is weak in the present scalar-wave setting, the results indicate that RD-derived patterns can serve as a useful self-organized platform for exploring directional dispersion tailoring beyond conventional lattice-based metamaterials.