Value noise (smooth randomness)

You blended two random values along a line. Now do it on a flat sheet: value noise is random numbers at the corners of a grid, blended smoothly in between. Five steps, all of which you have already seen:

1. i = floor(p) is the cell (whole numbers), f = frac(p) is the position inside it (0 to 1 in x and y).
2. Soften f: f = f * f * (3.0 - 2.0 * f).
3. Get a random number at each of the cell's four corners: a bottom-left, b bottom-right, c top-left, d top-right (hash(i), hash(i + float2(1, 0)), and so on).
4. Blend the bottom pair across: lerp(a, b, f.x). Blend the top pair across: lerp(c, d, f.x).
5. Blend those two results upward: lerp(bottom, top, f.y).

Move the sliders and watch the numbers: blend across twice, then blend up once. That is the whole algorithm. Then wrap it in a function called vnoise so you can reuse it. (Tip: the Outline button writes this plan into your editor as comments.)