Sometimes called Bowditch Curves, these patterns are produced naturally in tone analysis, which relies on a liquid medium and two tuning forks mounted at right angles to each other.  
Damping constants beta one and beta two of these special cases of the harmonograph are equal to zero, and they remain open if the ratio of the periodicity constants from the parametric equation that describes them is irrational.  Sometimes called Bowditch Curves, these patterns are produced naturally in tone analysis, which relies on a liquid medium and two tuning forks mounted at right angles to each other.  FTP, name these figures created by the addition of harmonics along the x and y axes of a cathode ray oscilloscope, named for a Frenchman who depicted multidirectional vibrations.
Damping constants beta one and beta two of these special cases of the harmonograph are equal to zero, and they remain open if the ratio of the periodicity constants from the parametric equation that describes them is irrational.  
Lissajous curves or figures