CorrNoise.jl is a Julia package to produce streams of correlated noise, i.e., random numbers which follow a 1/f distribution.
Here is an example showing how to generate 1/f noise with slope 1.7, knee frequency sampling frequency 0.05:
using Random
using CorrNoise
using Plots
rng = OofRNG(GaussRNG(MersenneTwister(1234)), -1.7, 1.15e-5, 0.05, 1.0);
data = [randoof(rng) for i in 1:10000]
plot(data)