Monofractals are simply not good enough

Continuing this post, this article reiterates my original inquiry on using monofractal structure within the model of hierarchical complexity. E.g.:

"Simple, straightforward linear models can exhibit the celebrated 'self-similarity' of fractals, that is, the similarity of a time series’ structures at many different scales. Cascade-like systems that demonstrate a patchwork of many fractional power-law exponents have more depth to them, exhibiting not simply similar structures at many different scales but also a contingency among these different scales" (209).