Dynamic Stability (Update)

I’ve hit a bit of a roadblock with the modeling side of reaction diffusion temporarily. Over the last week I spent a bit of time trying to understand SideFX Houdini, in order to use a definition which simulated a much more powerful reaction diffusion model. Unfortunately, tight time-frames probably mean I won’t be able to use it and need to search for alternative means.

This post is going to look into a little bit more of the theoretical side of the design (building on my previous discussion). I’ve been reading a book lately entitled How the Leopard Changed its Spots by Brian Goodwin. In a later chapter, Goodwin enters into a discussion about life at the edge of chaos. “For complex non-linear dynamic systems with rich networks of interacting elements, there is an attractor that lies between a region of chaotic behaviour and one that is ‘frozen’ in the ordered regime, with little spontaneous activity. Then any such system, be it a developing organism, a brain, an insect colony, or an ecosystem will tend to settle at the edge of chaos. If it moves into the chaotic regime it will come out again of its own accord; and if it strays too far into the ordered regime it will tend to ‘melt’ back into dynamic fluidity where there is a rich but labile order, one that is inherently unstable and open to change.”

This passage from the book I believe is the essence of the process I’ve been looking into. It speaks to the essence of emergent order. This also begins to tie in with Wolfram’s theories of Classes of complexity (1986). There are four classes:

  • Class 1 – patterns evolve into a stable state – all randomness is purged
  • Class 2 – Most of the patterns evolve into a stable or oscillating state – most of the randomness is filtered out, but some remains
  • Class 3 – patterns begin to evolve in a seemingly random manner, localised noise filters out much of the initial randomness
  • Class 4 – patterns reach extreme complexity, forming localised clusters of order, but all the while remaining chaotic for long periods of time

It is thought that reaction diffusion exhibits class 4 complexity, coined by Chris Langton (Chris Langton was one of the pioneers in the field of complex interactions and activity) as, “Life at the edge of complexity.” But it is this state of complexity that reaction diffusion exists in, this system is dynamic and changeable, it has a rich pattern of activity.

This is important for several reasons. As I’ve tried to reinforce before, the reaction diffusion process does not enter an equilibrium state. Essentially the four classes can be further grouped into 2 states, a) ordered systems which settle into an unchanging state, and b) where patterns produce extremely complex activities, separated by rules that result in partial ordering. State b also refers back to the u-skate boundary, where I initially discussed this idea. Furthermore, this also reinforces the idea of dynamic stability. While dynamic stability may seem counter-intuitive at first, this rather aptly rationalises the idea. The idea that elements are free to move from an ordered to an unordered state on their own accord without exerting themselves too far in either direction perfectly describes the behaviour exhibited by the reaction diffusion systems.

At this point, I need to modify my research question a little. What I realised is that my previous question implies a rather strict dependency on reaction diffusion, which I sense I may be moving away from in the coming weeks. Hence,

How can processes like reaction-diffusion inform architectural design?

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