Power Spectral Density — 1/f Flicker Noise
White noise, pink noise (1/f), Brownian motion (1/f²), and fractal signals
1/f noise (pink noise, flicker noise) appears ubiquitously: transistor noise, music, heartbeat intervals, earthquake magnitudes, stock prices, neural firing. Its power spectral density satisfies S(f) ∝ 1/f^α with α ≈ 1. Special cases: α=0 white noise (uncorrelated), α=1 pink/flicker noise, α=2 Brownian/red noise (integrated white noise), α=3 Violet-ish. Generation uses spectral synthesis: (1) draw random phases, (2) weight Fourier amplitudes by f^(−α/2), (3) inverse FFT. The log-log PSD plot shows the straight line with slope −α. The signal has fractal character with Hurst exponent H = (α−1)/2 for 1 < α < 3. The visualization updates in real-time as you drag α.