Value noise
The simplest lattice noise — random values at grid points, smoothly interpolated between — cheaper than gradient noise but with a more visible grid structure.
You assign a pseudo-random value to each integer lattice point and interpolate between them with a smooth curve, in practice a cubic or quintic smoothstep to avoid angular transitions. That is the whole idea: no gradient, no direction — just values being blended.
The difference from gradient noise such as Perlin noise and simplex noise, which instead interpolate random gradients and put their zero crossings on the lattice, is that value noise tends to clump axis-aligned and looks less organic. In return it is faster and easier to reason about. Summed in octaves — fractal noise, fBm — it still makes a serviceable basis for terrain and textures.