"Fractional Brownian Motion Simulation: Observing Fractal Statistics in the Wild and Raising Them in Captivity"
Jaymie Strecker 2004
Abstract
Fractals are shapes in which parts of the shape resemble the whole shape in some way. Brownian motion, a type of random walk, is a fractal. Fractional Brownian motion, a biased random walk in which the walker favors certain directions at each step, is also a fractal. Used to model a wide range of phenomena, from river levels and landscape topography to computer network traffic and stock market indicators, fractional Brownian motion is easy to find in natural processes but not as easy to simulate. This paper introduces a new simulation algorithm called fracture-stretch and compares its effectiveness to existing simulation algorithms.