I'm stumped trying to find a way to generate a 3-dimensional $1/f^\alpha$ noise time series. Basically I want simulate a forcing that is $1/f^\alpha$ in the 2 space dimensions and $1/f^\beta$ in time, $0<\alpha<2$ and $0<\beta<1$.
It believe I should be able to 3D fourier filter a giant random matrix, but the matrix sizes needed are around $512\times512\times2048$.
Does anyone know of a clever way to do this? Is fourier filtering my only option or is there some way to draw from a distribution so as to to generate these surfaces at each time step in a model, rather than creating and saving these giant matrices?
Any insight is appreciated!
