The self-similarity of fractals is indicated by the power-law relationship between their power spectral density and wave number, e.g. |X(k)|=Ck^(-b) where X(k) is the Fourier transform of surface elevation at wave number k and C and b are positive constants. b is often expressed as a Hurst exponent, H: b = 2H+1. 1) fractal_riverbed_4TU.m A Matlab script code to generate artificial fractal riverbeds with specified variables (e.g. Hurst Exponent, domain length, number of points, mininum wavenumber, roll-off wavenumber, ...) 2) artificial_surf1d_phaseC_4TU.m A Matlab function code to generate a power spectrum density and phase shift of a fractal riverbed. Input variables are Cq0 (maximum spectral density), H (Hurst Exponent), Lx (domain length), q0 (minimum wavenumber), qr (roll-off wavenumber1), qS (roll-off wavenumber2), qC (maximum wavenumber). 3) PSD_4TU.mat Power spectra of measured data (Martin, R. L., and D. J. Jerolmack (2013), Origin of hysteresis in bed form response to unsteady flows, Water Resour.