This class implements "improved noise" by Ken Perlin for 1D, 2D, 3D and 4D.

General noise is simply a collection of random values, like the random dot pattern on old TVs when there is no input signal. General noise is not smooth. Band-limited noise is a noise which is smooth. This can be generated by zooming into the noise pattern and applying a Gaussian blur. A more efficient version of band-limited noise is Perlin Noise.

Perlin Noise is a Gradient Noise: It use a grid of gradients. The noise is 0 at the grid points, i.e. for 3D Compute((int)x, (int)y, (int)z) == 0.

Between grid points the gradients are interpolated to created smooth noise. There is at most one oscillation between two grid points.

Perlin noise is consistent: For a constant position this method always returns the same noise value.

The resulting noise is scaled to keep values the range [-1, 1]. (This is only approximated using scaling factors determined by experimentation. Some returned noise values might still be outside [-1, 1].)

Random values are generated using a lookup table. Since the table is limited, the noise function repeats itself in each dimension after 256 values, for example:
Compute(x, y, z) == Compute(x + 256, y + 256, z + 256).

This class can also compute periodic/tileable noise for any integer period, such that:
Compute(x, y, z, periodX, periodY, periodZ) == Compute(x + periodX, y + periodY, z + periodZ, periodX, periodY, periodZ)

Reference