Generate higher dimensional pink noise

1D Pink noise, is easy enough to generate. See https://www.dsprelated.com/showarticle/908.php for example.

What about higher-dimensional pink noise, such as 2D or 3D pink noise? Is there an algorithm to generate that?

EDIT: One approach might be to simulate a natural process, since pink noise often arises in nature.

• Also see blog.demofox.org/2017/10/25/… – PyRulez Jul 24 '18 at 22:57
• You should be able to just apply a suitably shaped filter to white noise, or, equivalently, directly manipulate the signal in the frequency domain. That is, do a 2D Fourier transform, mutliply $\frac{X(\omega_x,\omega_y)}{\sqrt{\omega_x^2+\omega_y^2}}$, then do an inverse Fourier transform. Most likely you'll design your white noise to have $X(0,0)=0$ on average so you can just use $0$ instead of the divide by zero. There's also a normalization factor, but chances are you're normalizing the amplitude to fit in some range anyway. I haven't tried this, but this is the brute force solution. – Derek Elkins left SE Jul 25 '18 at 1:34
• What do you mean by 2D pink noise: $1/f$ or $1/{f^2}$? – Peter Taylor Jul 25 '18 at 7:53
• @DerekElkins the pixels may not have a uniform distribution then (individually), so it will be pink, but not noise. – PyRulez Jul 25 '18 at 13:46
• @PeterTaylor $1/f^2$, so each octave has equal energy (I think $1/f^2$ satisfies that). – PyRulez Jul 25 '18 at 13:47