Mandelbrot's fractal geometry has found a wide variety of applications. The statistical self-similarity of fractal shapes is inherent in the natural world and may be exploited to simulate natural processes. In particular, random fractional Brownian motion (fBm) corresponds to fractal landscapes and occurs widely in nature, accurately describing such phenomena as pitch variation in music, flicker noise in solid-state devices, and 2-D mountain landscapes.
In this paper [J16], we describe a novel way to generate fBm using 2-D recursive filtering techniques for the generation of fractal landscape images. The main improvement over current DFT-based techniques is that the coefficients of the filter can be spatially adapted to produce a variable "terrain" throughout the image. The landscape image example shown above is based on the spatially-variant 2-D recursive filters described in the this paper.