A Product–Delay algorithm for graphic design

A Product–Delay algorithm is presented for creating graphic designs on a computer. In this algorithm two functions u(t) and v(t) are multiplied yielding a function x(t). Another function y(t) is formed by delaying or advancing x(t) by a fixed amount of time t. These functions are evaluated over a suitable time interval and the results are plotted in the x–y plane. For appropriate choices of the functions and parameters, the x–y displays exhibit interesting geometric patterns. In this paper the algorithm is illustrated with a pair of sine and square waves. It is shown that a wide variety of graphic designs can be created with these simple waveforms. By virtue of its simplicity this algorithm can be programmed easily and quickly using general purpose software such as Maple, Matlab or Mathematica. It can be executed on standard platforms such as IBM PC compatibles, Macintosh computers or workstations. Some results in polar coordinates are also given.