Program note

Viewed from some angles, certain processes in nature may seem to be random and unpredictable, but when one's perception shifts, very definite patterns and ordered structures can be revealed. That is, there is a tendency for such processes to be "attracted"towards definite paths. Chaos theory calls such revelations "strange attractors".

High technology offers areas of work wherein there are no cultural boundaries, no shackles of tradition, and no stylistic constrains because herein lie all cultures and all traditions, with style defined by the blending.

This is indeed a very fine madness in which to seek method. The piece Strange Attractors was conceived as a search for attractors in just such a milieu.

Perhaps once certain
Through earth's dark curtain
A sometime glance
    would glimpse
        a vision
            far beyond
                the manufacture of frail
                    imaginings.

Then bedazzled
By unravelled mysteries
Blend at last
That all is universe.

Ian Fredericks

Notes on the computer graphics for Strange Attractors

The symmetric multi-coloured shapes projected from transparencies are, in the technical sense, strange attractors. They arose out of an ongoing study into symmetry creation and patterned turbulence by Mike Field (Mathematics, University of Sydney) and Marty Golubitsky (Mathematics, University of Houston). The chaotic or strange attractors are formed by iterating planar polynomial maps having various symmetries (that of a triangle, for example, or of a square). Such a map, with square symmetry, is

Here , a, b, and c are constants and z is a variable ranging over the complex plane. Each picture represents the result of plotting 50,000,000 or more iterates on a computer screen. Using prism software developed for the project,the number of times each pixel was hit was recorded and colours chosen appropriately. The pictures show that structure, in apparently chaotic systems, can form "on the average". The photographs were taken directly from Apollo and Sun workstation high resolution colour monitors.

The triangle with holes is called a Sierpinski triangle, and is a classic example of a fractal. It and the following image are generated by a procedure called "the chaos game", or "fractal tennis" (described in Scientific American, August 1990). This procedure involves following a point around the screen, as with the strange attractors, but since only a few thousand points need to be calculated the image can be generated during the performance.

The spidery shapes are generated by a modified version of the computer program described by the British zoologist Richard Dawkins in his book The Blind Watchmaker. Dawkins calls the shapes biomorphs, each being a recursively branching structure that approximates a fractal (it would be a true fractal only if the branching continued forever). The shape of the biomorph is controlled by 10 numbers, which Dawkins called genes. Changing these numbers is called mutation.

The biomorphs in Strange Attractors are created during the performance by a small computer. The genes are mutated at random by the program, so it is not known in advance what shapes will appear.

Mike Field and Gordon Monro

[The computer used in the performance was an Atari 1040.]

Performances, etc

• "Murmurs of Chaos" concerts by watt, Seymour Centre, University of Sydney, 27 to 29 September 1990.

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© Gordon Monro 2004.       Last modified: December 14, 2004.
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