Fractional Brownian Motion (2019)

In computer graphics and procedural terrain generation, Fractional Brownian Motion (fBM) plays a crucial role. fBM is a process where random increments are added to a position over time, creating paths that are statistically self-similar. The Hurst Exponent (H) controls the memory and integration of fBM, influencing its smoothness and fractal dimension. By incrementally adding noise signals of varying frequencies, fBM constructs self-similarity, mimicking natural shapes and textures. The parameter H determines the self-similarity of the curve, with values closer to 1 producing smoother results. The implementation of fBM involves an iterative process to generate deterministic randomness, with the parameter G (related to H) influencing the amplitude decay. Different values of H and G result in various types of fBMs, such as Pink Noise and Brown Noise. fBM's spectral characteristics make it efficient for modeling natural phenomena like terrains and clouds, outperforming methods based on sine waves. Understanding the interplay between H, G, and fBM parameters is essential for creating visually appealing and realistic computer-generated environments.