parametric equation

The butterfly curve can be defined by parametric equations of x and y. In mathematics, a parametric equation expresses several quantities, such as the coordinates of a point, as functions of one or more variables called parameters.

In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point. For this case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a surface, called a parametric surface. In all cases, the equations are collectively called a parametric representation, or parametric system, or parameterization (also spelled parametrization, parametrisation) of the object.