Generalized reaction-diffusion textures
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 tenser), 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. (C) 2007 Elsevier Ltd. All rights reserved.
reaction-diffusion texture synthesis generalized diffusion high-rank tensor