Complexity discussion

Speaking of the differences between the model of hierarchical complexity (MHC) and other forms of complexity (in this post), I recently had a discussion with Cory David Barker at the Commons Yahoo Adult Development Forum.* I inquired into the fractal nature of the MHC, since it uses a monofractal structure, i.e., recurring, self similar patterns. Multifractals though

"are more highly advanced mathematical structures: fractals of fractals. They arise from fractals 'interwoven' with each other in an appropriate manner and in appropriate proportions. Multifractals are not simply the sum of fractals and cannot be divided to return back to their original components, because the way they weave is fractal in nature. The result is that in order to see a structure similar to the original, different portions of a multifractal need to expand at different rates. A multifractal is therefore non-linear in nature."

Multifractals also better represent actual biological processes, whereas a monofractal structure "neglects rich cascade dynamics." Which reminds me of Zak and Tim's discussion of first and second simplicity, first simplicity being the monofractal nature of the MHC while second simplicity being multifractal constructions. Barker is working on using multifractals to upgrade the MHC.

* See this post and several following posts on this page and the next page.