Complementary N-Gon Waves and Shuffled Samples Noise
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.