Friday, August 23, 2013

Restricted and general fractal iteration

In this IPS thread I referenced Sara Ross's paper "Fractal model on non-linear hierarchical complexity." I wondering about these two sets of statements:

"Fractal means the repetition of self-similar patterns at different scales" (7).

"Every transition begins with some temporary equilibrium (A), regardless of when or where a transition occurs. This means transitions nested within transitions are ordered in exactly the same way" (8).

In the pomo/complexity and real/false reason threads complexity was differentiated between restricted and general varieties. This includes fractal chaos in the former variety, which it seems Ross is using. In the quotes fractals go from "self-similar" patterns to "exactly the same way." As I've explained elsewhere, actual fractals are themselves non-linear and while each iteration is similar it is also different, so not nested in "exactly the same way."* Not just the what of the content is behaving in a non-linear fashion but so is the math itself iterating non-linearly. While Ross wants a non-linear math to explain this process, i.e. the fractals and attractors of dynamic systems, she is still using the more restricted varieties of Bertalanffy and Mandelbrot instead of the more general versions of Prigogine and Cilliars (and DeLanda, Morin and Deleuze).

See this post for a critique of Mandelbrot's kind of complexity. And this one with Morin discussing the two varieties. From the latter:

"Restricted complexity refers mainly to the mathematical and computational approaches to complexity, often strongly informed by chaos theory. This approach, Morin argues, acknowledges the non-linear, relational nature of complex systems, but seeks to tame it in ways which reintroduces positivism and reductionism. General complexity on the other hand, argues for the limits of all approaches to complex systems and urges that we acknowledge these limits and recognise that we need a new language in which to do this, a language which moves beyond Enlightenment ideals of neutrality and objectivity."
* Hence those pretty and symmetrical computer-generated pictures of fractals using formal bifurcations. Real fractals generate a self-similar yet novel iteration at each temporary equilibrium.

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