Centre of Attraction

You get periods where there is no pattern, and then you get into an area where you get a particular pattern, and then you get into no pattern again. It’s a bit like old fashioned radios, where you tune the radio set and get a station, and then there’s a noise in between, and then you get the next station. You come in and out of these resonant frequencies.

These are like basins of attraction. [There are] patterns that we get at [certain] frequencies, and [there is a] minimum amplitude needed to create the pattern […] There is a point where you get the pattern clearly with a minimum of energy and there is an area around it where you have to have more energy to make [the pattern] happen.

If you look at the vibrations at these bits in between, what you see is something on the cusp... It’s what Chaos mathematicians call a ‘chaotic pattern’, where it is drawn between two attractors.

The in-between is an unstable area.

[Rupert Sheldrake]
Dynamic Patterns in Water as Analogue Models

That’s a hallmark of truth - it snaps things together.

People write to me all the time and say that, “It’s as if things were coming together in my mind.” Well, that’s what archetypes do, [they] glue things together. The proper expression of unconscious being teaches people what they already know. It’s like the Platonic idea that all learning is remembering.

You have a nature. And when you feel that nature articulated […] it’s like bringing the levels of being into synchrony, that’s what you feel. What [you] think, and what [you] feel have come together. And you feel that ‘snap’ [into] a simpler state, [and you’re] not rife with contradictions any more.

[Jordan B. Peterson]
'Jordan B Peterson | *NEW 2017* | full-length interview'

While studying turbulence, physicist David Ruelle (1971, 1980), coined the term strange attractor to describe the tendency of systems to move toward a fixed point, or to oscillate in a limited repeating cycle.

A pendulum is a good example of a fixed point attractor. It moves closer to its steady state over time, as it gives up energy to air friction.

Strange attractors imply that nature is constrained. The shape of chaos unfolds relative to the properties of the attractor.

An interesting property of the strange attractor is that initial conditions make little difference. As long as the starting points lie somewhere near the attractor, the system will rapidly converge upon the strange attractor. 

[David S. Walonick]
'General Systems Theory'

The direction of self-organization is always away from disorganized complicatedness and toward more organized complexity. "Greater levels of performance" thus refers to more efficient processing of energy and matter flows, all in the service of the enhanced integration and cohesion of the whole. 

Autocatalysis's "goal" is its own maintenance and enhancement in the face of disintegrating pressures from the environment. It is to that extent partially decoupled from and independent of the environment: autonomous.

Commentators on Aristotle's concepts of formal and final cause have often noted how these become entangled in living things. As we saw, Kant identified teleology with self-organization: an intrinsic physical end such as a tree both produces itself and maintains itself as itself, that is, it aims to preserve and promote its overall identity despite a constant turnover of components. 

This description is obviously true of dissipative, autocatalytic processes. As they select for inclusion in the web molecules that enhance overall activity, autocatalytic cycles "aim" at greater performance by constantly pruning and streamlining their pathway structure. To maintain itself as itself, an autocatalytic web functions as an "attractor": a rudimentary precursor of final cause.

[Alicia Juarrero]
Dynamics in Action, p.127

All attractors represent characteristic behaviors or states that tend to draw the system toward themselves, but strange attractors are "thick," allowing individual behaviors to fluctuate so widely that even though captured by the attractor's basin they appear unique. 

The width and convoluted shape of strange attractors imply that the overall pathway they describe is multiply realizable. 

Strange attractors describe ordered global patterns with such a high degree of local fluctuation, that is, that individual trajectories appear random, never quite exactly repeating the way the pendulum or chemical wave of the B-Z reaction does. 

Complex systems are often characterized by strange attractors. The strange attractors of seemingly "chaotic" phenomena are therefore often not chaotic at all. Such intricate behavior patterns are evidence of highly complex, context-dependent dynamic organization

[Alicia Juarrero]
Dynamics in Action, p.155

One mark of such complexity is that variations in behavior are often not noise at all: irregularities can signal the presence of a strange attractor. When behavior is constrained by a such an attractor, it is the variations that are interesting, for there, lurking behind what at first glance appears to be noise, complex dynamic attractors are in play. 

The more general and abstract the intention, the more complex the behavior allowed. 

One significant advantage of a complex dynamical systems perspective, therefore, is that it can account for differences and irregularities in behavior, which covering laws (and a fortiori behaviorism) could not.

[Alicia Juarrero]
Dynamics in Action, p.222

Strange attractor: Low resolution, permissive of variation, pattern not necessarily discernible until zoomed out. A vague centre.