How to create 2D (directional) noise?

Question

I'm just getting started trying to understand noise generation algorithms. What I'm trying to achieve is to get a 2D (or 3D) grid of random directional vectors (again, 2D or 3D) according to a noise distribution like Perlin, ie. not just a grid of totally randomly generated vectors (which would be easy to do).

Before starting to figure this out, I had assumed that 1D noise functions would be those that produce a series of float values (ranging from -1 to 1, for example), and that 2D noise functions would produce float2 values, 3D noise would produce float3 values, and so on.

However, searching for so-called 2D noise functions, it seems that they are used to produce a 2D grid (ie. texture) of single float values. However, what I'm looking for is a 2D grid of 2D (float2 / vector2) values, or a 3D grid of 3D (float3 / vector3) values.

From my (still pretty limited) understanding of a gradient-based noise like Perlin, I feel like I could probably hack something together from an existing Perlin function - doing a bi-linear/tri-linear interpolation of the surrounding gradient vectors which are ordinarily used for the subsequent dot product in Perlin noise. But I have no idea if that's the correct approach.

Are there existing libraries/methods for something like this?

Answer 1

Why don't you just use Perlin noise twice on the same grid, or volume? Each with slightly different parameters (a phase shift, or different pseudo-random vectors). In this case both component of your float2 are smoothly defined by a Perlin Noise field. A float2 $v$ could be defined as $v = \{P(u,v), P(u+0.5, v+0.5)\},$ where $P(u,v)$ is the Perlin noise function. However, this will make the $x$ and $y$ component of $v$ very close depending on the scaling of the grid values.

Answer 2

You can use the gradient of the noise/hash which for a function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ would be $n$ dimensional (depending on the application this may not work for you). Another possibility, as Reynolds mentioned is to generate the noise by calling the function multiple times.