The code examples have me confused because they return a single sample at a time, but if noise is to have the kind of different characteristics discussed at different scales, individual sample values cannot be independent of previous sample values.

I guess the provided code examples must return values which are ordered somehow by properties of the `noise` function, which must involve some memory of previously given values. But this function is described as:

>some noise function of our choice... the choice doesn't matter much

The nature of that function is really essential, if it has any independent random distribution, the examples will just return values with an independent random distribution that is bell or triangular or spike shaped.

The basic method of creating a sequence which has different variability at difference scales is to create separate random walks, scale (resample) them and then sum them together. This can be optimized by generating the component walks (with different scales) on the fly, but there is no way to create such a sequence on the fly from a function which returns values which are independent of the sequences previous values.