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 equilibrium, 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.