You need a deterministic function for at least 1 milion values that returns enough noise over them (since you have a determined index for every pixel).
Pretty close to this volatilism demand might be goniometric function , for which you pick period size and way to volatilize y values on sufficient defintion length.
If you reduce to 100000 values and pick definition 0.0-100.0 then x would be multiple of index and constant 1/100.0. You than may decide to volatilize 10 periods of goniometric function by polynome of 10th degree (20 multiplications) - this randomizing polynome is predefined and does not change.
You can pick period size and polynome size/period size, what allows you to scale the noise and stereotype size.
There are more ways how to achive noise. You may also volatilize polynome definition (its constants) upon index (still determined), or you can experiment with closest prime number to index.