The floor of the repeated domain gives a unique integer ID per tiled instance for per-cell variation

When a domain is tiled with mod(p, period), the floor of p/period gives an integer cell coordinate that is unique per repetition. This ID seeds pseudo-random values (via a hash or aliased sine) to vary size, color, and displacement between otherwise identical copies. The pattern mirrors the parabola-jump technique: fractional part = where in the cycle; integer part = which cycle. Without per-cell IDs all instances are identical and the scene reads as synthetic.

Examples

vec2 cellID = floor(pos.xz / 3.0); float rnd = sin(dot(cellID, vec2(127.1, 311.7))) * 43758.5; float radius = 0.5 + 0.3*fract(rnd); — different size per cell.

Assessment

Explain why using sin(cellID.x * 127.1) alone (not a dot product with a second dimension) would produce identical variation along one axis.