Chapter 4: Systems Based on Numbers

Section 6: Mathematical Functions

Lissajous figures

Plotting multiple sine functions each on different coordinate axes yields so-called Lissajous or Bowditch figures, as illustrated below. If the coefficients inside all the sine functions are rational, then going from t = 0 to t = 2 π Apply[LCM, Map[Denominator, list]] yields a closed curve. Irrational ratios of coefficients lead to curves that never close and eventually fill space uniformly.

From Stephen Wolfram: A New Kind of Science [citation]