GENWiki

               Chaos, Strange Attractors and BrainMaker Plots

  Take the last 200 years' data on cotton production.  Plot a point which
  is one years' production versus the next years'.  You get data points
  scattered all over the screen like stars at night.  If you were to plot
  A LOT of points (without lines connecting them) you get a shape, like a
  donut.  The points seem to fall on or near a circle.  This is a Strange
  attractor.

  In a Normal or Real attractor, you get dense collection of points in the
  middle and spreading out fading out.  The price has an equilbrium, the
  production has an equilibrium, represented by the dense collection
  around a single point.  A Strange attractor is an attractor for which
  there is not an equilibrium point.

  There is no math currently that explains the plot of something versus
  something else which produces the donut.  The presence of a Strange
  attractor means you're dealing with a chaotic system.  A chaotic system
  is a nonlinear feedback system.  In the chaotic cotton production
  system, what you learn by seeing the Strange attractor is that there is
  some sort of a feedback mechanism, there is an analytic solution to what
  the system is doing and there is feedback around the analytic solution.

  You get Strange attractors when you look at the population of foxes over
  the years as it grows and shrinks.  This is chaotic, rather than random.
  In a random system, you get points scattered all over with no shape
  whatsoever and there is no underlying mechanism, therefore no way to
  predict anything.  In a chaotic system there is an underlying mechanism
  with nonlinearity and feedback.  It is believed by some that because
  there is an underlying mechanism analytic approaches can be used to make
  predictions.

  With BrainMaker Professional you can make plots to find Strange
  attractors.  In Netmaker you put cotton price in a column, cotton price
  shifted down by one in another, plot one on the X and one on the Y.
  Plot lots of months worth of data.  You will see a donut, a Strange
  attractor, which indicates an underlying mechanism with nonlinearity
  and feedback. If you discover the underlying math that explains this,
  please call us immediately.