Take the integral of white noise: the frequencies you have left are red noise, named because energy is in the lower frequencies of the power spectrum. It’s also called Brownian noise, because it can be derived from the drunkard’s walk of Brownian motion.

For a good overview of all things noise generation, check out this page on Noise Functions and Map Generation from Red Blob Games. It’s got a bunch of examples of different types of noise (with Python source code) and has a bunch of suggestions for how to use noise for different effects.

For more about the colors of noise, check out this explanation from a signal processing expert.