Chaos/Strange Attractors
We can take a step away from our internal state of anxiety and our intimate experiences of nothingness and non-being. We find that the natural world in which we live is filled with dynamic pulls that seem to emanate from nothing in particular.
Attraction: another of our guides to the world of nothingness, John Van Eenwyk (1997) identifies these pulls as what chaos and complexity theorists call “strange attractors.” He approaches the challenging topic of strange attractors by first offering a general description of attractors in the natural world (Van Eenwyk, 1997, p. 53):
“‘Attractor’ is a general term used by mathematicians and physicists for any pattern that defines the repetitive motion of a system. For example, a pendulum that is subject to friction eventually stops swinging. The point directly underneath it when it stops is called a single-point attractor, for it appears to attract the pendulum’s motion on each successive swing, eventually bringing it to rest over that point. A pendulum not subject to friction swings back and forth in a continuous manner, constantly tracing out the same pattern of motion. This is called a limit-cycle attractor.
There are other kinds of attractors (for example, those that rotate on an axis while revolving around a center, tracing a doughnut shape called a torus) that settle into discernible patterns, which consistently recapitulate themselves as they retrace their paths (circle, ellipse, torus, etc.).”
Van Eenwyk (1997, p. 53) now turns to more intriguing complex attractors:
“Complex-or chaotic-dynamics, while they do settle down into patterns that are recognizable, never retrace the same path. Because chaotic systems can be analyzed mathematically, they can be represented on a graph. These bear little resemblance to the familiar graphs of lines, planes and solids, however. Instead, they contain multiple bifurcations that double back upon themselves in bizarrely repetitious fashion. Expressed in the language of geometry, chaotic dynamics are simply spectacular. The images produced portray complex patterns, or attractors, of chaotic movement captured in time and space. These patterns are called strange attractors, for they reflect the bizarre configurations into which complex dynamics settle.
The word “attractor” here is somewhat of a euphemism, suggesting that the patterns into which the iterations of mathematical functions settle themselves have actually attracted the iterations of those functions. But “strange” accurately describes these patterns, for while discernible as such, they are so complicated that they transcend the usual categories associated with patterns.”
Van Eenwyk (1997, P. 54) offers an additional distinction regarding the unique nature of strange, complex attractors:
“Unlike regular attractors, which settle into repetitive cycles of limited size, strange attractors contain “isolated orbits . . . [that display] no orbital stability . . . the future behavior [of which] has a sensitive dependence on initial conditions.” [K Teomia, “Periodically Force Non-linear Oscillators, “ in A. V. Holden, et. Chaos, p. 218). Never repeating—yet always resembling—themselves.”
