Generalized reaction–diffusion textures

Abstract

We present a method of synthesizing textures based on a modified reaction–diffusion equation. A non-Gaussian model of diffusion is employed to make a new class of textures possible. Whereas the Gaussian diffusion model is characterized by its covariance matrix (a rank-2 tensor), the generalized model of diffusion is characterized by a sequence of tensors of increasing rank which represent higher-order moments of the diffusion displacement probability. A numerical method of solving the new reaction–diffusion equation is described, as well as representative textures generated by this technique. The resulting patterns are inorganic in nature, often featuring sharp corners. The generalized reaction–diffusion textures display spatial inhomogeneity, even when the diffusion process is homogeneous, making it possible to generate complex textures from few parameters when compared with previous techniques employing inhomogeneous reaction–diffusion. The preferred orientations depend on the tensor sequence, and can be inspected prior to texture generation by plotting the non-Gaussian diffusion propagator.