Playing with Chaos

Discussion created by KJBob on Sep 12, 2016
Latest reply on Sep 30, 2016 by KJBob

     Chaos theory, that is.  This interesting branch of mathematics describes why a system's behavior can appear random and unpredictable, despite its being quite deterministic.  Wikipedia's entry features several examples of chaotic systems -- one of which is an electronic circuit consisting of op-amps, resistors, caps, and diodes.  As it turns out, this circuit is easily translated into SigmaDSP blocks, which can run on a ADAU1701:



     It amounts to a lowpass filter with gain, two integrators, and an absolute value standing in for the diodes.  It solves a third-order, nonlinear differential equation (can anyone say, "analog computer" -- yes, sometimes I feel as old as my avatar!).  With the right amount of gain this goes chaotic, resulting in an output like this one:



     Chaos theory explains why we can hardly predict the weather beyond about one week, even with sophisticated computer models programmed with known laws of physics.   And why Jurassic Park was doomed to terrible failure.