Attractors



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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


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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'


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Related posts:
The Colour Wheel
The Eternal Ideas
Escaping Uncertainty
In-between
Shades of Gray

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