Chladni-Inspired Aesthetic Patterns: A Flexible Parametric Model from Thin-Plate Vibrations.

We introduce a physics-based parametric generative model for a class of wave-like, organic aesthetic patterns that streamlines the conventional two-stage design workflow. Unlike conventional approaches that rely on separate texture design and manual invariant mappings for seamless tiling, our method simultaneously derives texture and layout from the explicit solution of the thin-plate vibration equation. By encoding symmetry and tiling constraints directly as boundary conditions, the model inherently guarantees seamless, symmetric patterns without ad-hoc mapping functions. Within this framework, artists can intuitively control style and structure through a compact set of visually interpretable parameters, enabling efficient generation of diverse periodic and aperiodic tilings. Extensive experiments validate the method's efficiency, structural coherence, and stylistic richness, demonstrating clear advantages over conventional approaches in both visual diversity and structural integrity. This work offers a novel, interpretable, and efficient approach to controllable digital art creation.