32 Using a Circular Lindenmayer-System to Create Polyphonic Music Compositions in Real Time
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Lindenmayer-systems (L-systems) are a specific type of fractal algorithm that incorporates a formal grammar of symbols and replacement rules. The authors have developed an L-system variant called a circular L-system (CL-system) that enables real-time mapping of a continuous data stream into polyphonic music. Polyphony in the system is created in a way similar to branching schemes used in graphical interpretations of bracketed L-systems. Most graphical interpretations of L-systems apply interpretations to only the top-most member of the stack, so the evolution of a branch occurs linearly, and no other portion of the system is evolved while developing that branch. In a sonic situation, this is equivalent to allowing only one voice at a time, but allowing many voices sequentially. To achieve polyphony in the current system, interpretations are applied in parallel to all members of the stack, thus allowing the evolution and rendering of multiple voices simultaneously.