Complementary N-Gon Waves and Shuffled Samples Noise

Dominik Chapman
DAFx-2020 - Vienna (virtual)
This paper introduces complementary n-gon waves and the shuffled samples noise effect. N-gon waves retain angles of the regular polygons and star polygons of which they are derived from in the waveform itself. N-gon waves are researched by the author since 2000 and were introduced to the public at ICMC|SMC in 2014. Complementary n-gon waves consist of an n-gon wave and a complementary angular wave. The complementary angular wave introduced in this paper complements an n-gon wave so that the two waveforms can be used to reconstruct the polygon of which the waveforms were derived from. If it is derived from a star polygon, it is not an n-gon wave and has its own characteristics. Investigations into how geometry, audio, visual and perception are related led to experiments with complementary n-gon waves and a shuffle algorithm. It is possible to reconstruct a digitised geometric shape from its shuffled samples and visualise the geometric shape with shuffled samples noise signals on a digital display device or also, within some limitations, on an oscilloscope in X-Y mode. This paper focuses on the description of discrete complementary n-gon waves and how a Fisher-Yates shuffle algorithm was applied to these waveforms and used to create the shuffled samples noise effect. In addition, some of the timbral and spatial characteristics of complementary n-gon waves and shuffled samples noise are outlined and audiovisual applications of these waveforms briefly discussed.