Named noise colors (pink, brown, yellow) map to specific fBm spectral slopes and Hurst exponents

fBm spectral density follows a power law f^(-B) where B = 2H+1. In log-log plots, this appears as a straight line with slope -B (dB per octave = -(3B)). This connects computer graphics fBm to the signal-processing naming convention for colored noise: H=0 (G=1) is Pink Noise (f^-1, -3dB/oct, sounds like rain); H=0.5 (G=0.707) is Brown Noise (f^-2, -6dB/oct, indoor rain); H=1 (G=0.5) could be called ‘Yellow Noise’ (f^-3, -9dB/oct, engine-behind-door quality) and is the terrain-generation standard. Graphic programmers often ignore H and hardcode G=0.5 without knowing they are producing Yellow Noise. Understanding the color taxonomy helps reason about when to deviate from G=0.5 for stylized effects.

Examples

Pink noise (H=0, G=1): useful for rougher, more chaotic textures (volcanic, weathered). Brown noise (H=0.5): stock-market-like randomness. Yellow noise (H=1, G=0.5): smooth isotropic terrain, clouds, realistic organic surfaces.

Assessment

A shader artist wants to create a texture that looks rougher and more random than standard terrain fBm. Should they increase or decrease G? Justify using the H-G-spectral-slope relationship.