Music

 

Strange Attractors & Logarithmic Spirals (2001, rev. 2006)
a computer-generated composition

Download: mp3 (9:27)
Format: mp3, 128 kbs, 44.1kHz, joint-stereo

Strange Attractors & Logarithmic Spirals (2001) was executed in Csound, a digital audio signal processing environment by Barry Vercoe. The work sets into opposition sonic manifestations of two beautiful mathematical forms: strange attractors, chaotic systems that cycle periodically, yet never repeat exactly the same pattern; and logarithmic spirals, a perhaps more familiar shape found throughout nature in shells, sunflowers, galaxies, tusks, etc. This spiral has a long distinguished history as a source of inspiration for artists and its connections to the golden proportion and Fibonacci series are explored in this work.

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More about Strange Attractors & Logarithmic Spirals

The Lorenz Attractor, a strange attractor first discussed by M.I.T. scientist Edward Lorenz (Lorenz 1993), is shown in Fig. 1.

Fig. 1. The Lorenz Attractor.

When initialized with a special set of values, a graph of this system produces the beautiful butterfly-shaped pattern shown above.The sound quality of the Lorenz Attractor instrument varies from noise-like clicks to percussive zips and buzzes.

The Risset instrument, on the other hand, generates sounds of an entirely different nature. A truly ingenious additive synthesis technique is used to produce a cascading arpeggio of the frequency components of a given complex waveform. The frequency content and rate of the arpeggio can be very precisely controlled. The sustained sounds produced by this instrument vary from organ-like timbres to sound not unlike those produced by a Tuvan throat singer. The sonified Lorenz Attractor and Risset cascading arpeggios serve as the main poles of opposition in this work.

References

Richard Boulanger, ed., The Csound Book (Cambridge, MA: MIT Press, 2000), 379-80.

John-Philip Gather, ed., Amsterdam Catalogue of Csound Computer Instruments (ACCCI), Instrument 02_43_1.

Mario Livio, The Golden Ratio (New York: Broadway Books, 2002).

Edward Lorenz, The Essense of Chaos, (Seattle: WA: 1993), pp. 188-89.

Links

Mikelson's Lorenz Attractor instrument is discussed by Richard Boulanger at: <http://www.csounds.com/mastering/em_10.html>.

The Csound code for the Lorenz Attractor instrument may be obtained at: <http://www.csounds.com/mikelson/>

Learn more about the golden ratio at: <http://mathworld.wolfram.com/GoldenRatio.html>

Learn more about the connection between the Fibonacci sequence and golden ratio at: <http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html>