Lissajous Curve Tracing Algorithm

Lissajous curves are a family of curves described by the following parametric equations:

Lissajous curves have applications in physics, astronomy, and other sciences. Below are a few examples of Lissajous curves that you will be able to reproduce in the Python Trinket provided below by changing the values of constant A and B in the Python code.

Lissajous Curve using Python Turtle

Spirographs?

When tracing different Lissajous curves, you will notice that these curves are enclosed in a rectangular shape.

Spirographs are very similar to Lissajous curve but instead of being enclosed by rectangular boundaries, spirographs are generally enclosed by a circular boundary.

You can trace your own spirographs using Python Turtle by completing this Python Turtle challenge.

Rose Curves

Your task is to adapt the above Python script to draw different Rose curves. You can find out more about rose curves and about their parametric equations on the following wikipedia page.