41 lines
2.4 KiB
Plaintext
41 lines
2.4 KiB
Plaintext
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Chaos, Strange Attractors and BrainMaker Plots
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Take the last 200 years' data on cotton production. Plot a point which
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is one years' production versus the next years'. You get data points
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scattered all over the screen like stars at night. If you were to plot
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A LOT of points (without lines connecting them) you get a shape, like a
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donut. The points seem to fall on or near a circle. This is a Strange
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attractor.
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In a Normal or Real attractor, you get dense collection of points in the
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middle and spreading out fading out. The price has an equilbrium, the
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production has an equilibrium, represented by the dense collection
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around a single point. A Strange attractor is an attractor for which
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there is not an equilibrium point.
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There is no math currently that explains the plot of something versus
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something else which produces the donut. The presence of a Strange
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attractor means you're dealing with a chaotic system. A chaotic system
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is a nonlinear feedback system. In the chaotic cotton production
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system, what you learn by seeing the Strange attractor is that there is
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some sort of a feedback mechanism, there is an analytic solution to what
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the system is doing and there is feedback around the analytic solution.
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You get Strange attractors when you look at the population of foxes over
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the years as it grows and shrinks. This is chaotic, rather than random.
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In a random system, you get points scattered all over with no shape
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whatsoever and there is no underlying mechanism, therefore no way to
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predict anything. In a chaotic system there is an underlying mechanism
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with nonlinearity and feedback. It is believed by some that because
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there is an underlying mechanism analytic approaches can be used to make
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predictions.
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With BrainMaker Professional you can make plots to find Strange
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attractors. In Netmaker you put cotton price in a column, cotton price
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shifted down by one in another, plot one on the X and one on the Y.
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Plot lots of months worth of data. You will see a donut, a Strange
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attractor, which indicates an underlying mechanism with nonlinearity
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and feedback. If you discover the underlying math that explains this,
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please call us immediately.
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