Lissajous Curves

About this plugin

Lissajous curves, named after the French mathematician Jules Antoine Lissajous, are mathematical visualizations that represent the motion of two perpendicular harmonic oscillations. These curves are formed by plotting the coordinates of points that correspond to the simultaneous values of the two oscillating variables.

The shape and pattern of a Lissajous curve depend on the relative frequencies, phases, and amplitudes of the two oscillations. By adjusting these parameters, a wide variety of visually captivating curves can be generated. Lissajous curves can exhibit symmetric or asymmetric patterns, including ellipses, circles, straight lines, and more intricate looped or spiraling designs.

Lissajous curves have applications in various fields, including mathematics, physics, engineering, and art. They are used for visualizations, harmonic analysis, signal processing, and even in graphical representations of sound waves. In the world of design, Lissajous curves offer an aesthetically pleasing and intriguing element that can be incorporated into logos, backgrounds, illustrations, and other creative projects.

Plugin details:

• a: This is the frequency of oscillation along the x-axis for the Lissajous curve. The value of 'a' influences the shape and complexity of the curve, determining how many 'loops' it forms in the horizontal direction.

• b: Similar to 'a', 'b' is the frequency of oscillation along the y-axis. It determines how many 'loops' the curve forms in the vertical direction.

• delta: This is the phase shift between the two sinusoidal functions that generate the Lissajous curve. By altering the value of 'delta', you can change the relative positions of the curves in the x and y directions, leading to a wide variety of different shapes.

• numPoints: This is the number of data points used to draw the Lissajous curve. It's effectively the resolution of the curve; a larger number of points will result in a smoother curve, while fewer points will create a more 'stepped' or polygonal appearance.

• scale: This is a scaling factor that influences the overall size of the Lissajous curve. By adjusting 'scale', you can make the curve larger or smaller without changing its basic shape.