Chaos As Social Order

fixed points in maps, limit cycles, or a toroidal surface for quasiperiodic motions, are all classical dynamical attractors” (261).  The attractor pattern is an equilibrium state or set of states to which a dynamical system converges.  An attractor is not necessarily either one or many states exclusively.

            The verbal phrase “to which…converges” conveys this non-dualistic quality and also points toward the quality of an attractor that makes it strange:  a final equilibrium is never reached–symmetry is never reached, nor is a “stable” asymmetry reached.  The pattern shows self-similarity across scales but it never reaches an identity, or, equilibrium condition.  Using Moon again, a strange attractor is “the attracting set in phase space on which chaotic orbits move.  An attractor that is not an equilibrium point nor a limit cycle, nor a quasiperiodic attractor.  An attractor in phase space with fractal dimension” (267).

            A strongly defining characteristic of a strange attractor, moreover, is sensitive dependence on initial conditions.  The pattern of a strange attractor may be taken as the pathways of points that begin at arbitrarily small distances from each other.  Over time, those distances change so much and so quickly that at a later time in the pattern the initial conditions are no longer observable.  The later state of the pattern or system cannot therefore be connected deterministically with the beginning state.

            It has been proven repeatedly in both numerical and physical experiments that such a pattern must involve simultaneous folding and stretching.  For example, you put a spot of dark blue dye on the surface of a large lump of white

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