# the butterfly effect

In his book *Chaos: Making a New Science*, author James Gleick describes * The Butterfly Effect* as:

…the notion that a butterfly stirring the air today in Peking can transform storm systems next month in New York.

(Gleick 1987)

This work attempts to breathe life into that metaphorical butterfly. Gleick’s quote captures the spirit manifest in the chaos theory, especially, the theory of sensitive dependence on initial conditions described by scientist Edward Lorenz. Lorenz was using primitive computer models of weather systems to investigate his intuitive notions about the order he perceived in seemingly disorderly weather systems, when he discovered that a very small adjustment in the input of a system could produce large-scale consequences in the output.

Represented in the work by a continuously sweeping glissando gesture, the butterfly is controlled by a live performer who interacts with the Doppler equation to control the pitch trajectory of the glissando. Named for Austrian physicist Christian Doppler (1803-1853), the Doppler equation describes the pitch we perceive when we encounter a moving sound source like a passing train.

It is interesting to note that the Doppler equation was first tested experimentally in 1845 "using a locomotive drawing an open car with several trumpeters” (Walker *et al. *2008). Equation (1) gives the Doppler equation for moving source and stationary detector, however, for the recorded version I chose to move the audience around the butterfly. This type of decision may easily be made "on the fly" in a programming environment like Cycling 74's Max/MSP, the tool I utilize to create my real-time interactive compositions. The Doppler equation for a stationary source and moving detector is:

When the detector is stationary, the butterfly emits a 440 Hertz tone. Under the influence of the performer's control, however, the butterfly’s pitch sweeps up and down according to equation (2). Any control device that produces a continuous range of values between 0 and 127 may be used to supply the input values for V_{d}. Finally, the output values for *f* ' are scaled to fall within an octave boundary interval: A4–A5, or 440-880 Hertz.

The butterfly’s improvised flight is set against a deceptively simple sonic landscape: a Fibonnaci-inspired ostinato figure whose spectral content and spatial location are in constant flux. The work was realized on an Emu UltraProteus synthesizer. This synthesizer’s Z-plane filter technology allows the composer to interpolate between two complex spectral filters using a single Morph parameter, as well as use five different chaotic function generator curves to dynamically change the filter over time.

RB

### references

E-mu Systems, 2003. *Proteus X Operation Manual*. Scotts Valley, CA.

http://www.emu.com/support/files/storage/ProteusXOpEN.pdf

Gleick, James 1987. *Chaos: Making a New Science*. New York: Penguin, p. 8.

Walker, Jearl, David Halliday and Robert Resnick, 2008. *Fundamentals of Physics*, 8th ed.

New York: Wiley, pp. 460-463.

Weisstein, Eric W., 2009. "Chaos." From *MathWorld*--A Wolfram Web Resource.

http://mathworld.wolfram.com/Chaos.html

Updated: January 12, 2012