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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.