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| WaveWarp 2.0 Example DrawingBoard
VisualisationOfChaosExample1
Description
Visualisation of Chaos Example 1
Illustrates the use of the Audio Phase-Space Scope for real-time phase-space plotting of the two output states from the
Henon Strange Attractor (the basis of the Chaotic Control Generator 2). Play the DrawingBoard and observe the real-time
evolution of this classic phase-space trajectory.
The "strange attractor" is named so because the trajectory remains forever bounded, as evident in the scope, though it
never repeats itself exactly. In other words, the states are "attracted" towards the bounded regime. They repeatedly cycle
around without ever precisely re-tracing their tracks.
This can lead to interesting music connotations, since, by definition, music consists of almost periodic sequences of
almost-periodic sounds!
In this example, the outputs of the strange attractor are simply multiplied together, amplified, smoothed, then fed into the
Controllable Combo Oscillator to control its frequency. The result is an "alien hum" which is not completely periodic.
Experiment with all settings of all components to and enjoy the chaos in the process.
[Refs: (1) "Introduction to Applied Mathematics", Gilbert Strang, Wellesley-Cambridge Press, 1986. p 504-505.
(2) "Chaos: making a new science", James Gleick, Penguin Books, 1987, p 149-151.]
one audio signal versus another.
In this example, a chaotic wave (produced by the Controllable Combo Oscillator driven by the Chaotic Control Generator 1)
is passed through a Moorer Comb filter (a key element of IIR-based reverbs) and plotted against a delayed version of
itself.The interesting thing to note is how the shape of the plot (in the Audio Phase-Space Scope) has a regular pattern but
yet never repeats itself. This is a hallmark of chaotic systems.
Try increasing the gains of the Moorer Comb filter. Interesting musical sounds will emerge (due to the reverberant effect of
the comb filter).
Components used:
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