Random Fourier Features

The blue surface is the Gaussian kernel, k of x and y, with x fixed at the origin: one at the centre, falling to zero with distance.

Bochner's theorem writes it as an average of waves: the expected cosine of omega transpose x minus y, with the frequencies omega drawn from a Gaussian. Each orange dot on the floor is one frequency.

The rest of the narration is in the book's Companion.