Lissajous curves describe complex harmonic motion and are defined by parametric equations of two sinusoidal functions (represetned by the circles in the animation). The numbers inside the circles express their relative speeds, which is also represented by their colors.
To improve efficiency in drawing, simpler curves are approximated by fewer lines. Since the intersection points are only calculated periodically, it makes some curves with small periods look jagged. In reality, these curves would not have such rough corners. If you have a more powerful computer, try changing the parameters below for smoother shapes.
You can export a high-quality version of the render using the button below.
Try changing the parameters below to see different curves. Note: this depends on your computer's performance. The following changes will require more computing power: more circles, fewer frames between calculations, smaller size multipliers, fewer frames between circle rerenders.
Number of circles:
Top circles' starting position (in multiples of pi):
Left circles' starting position (in multiples of pi):
Max. frames between calculations:
Frames between calculations size multiplier:
Frames between circle rerenders:
See the results!