Harmonics | Simulated harmonograph - 2D The equation that describes a harmonograph is essentially the relationship between two decaying sine waves. The Lissajous Curves [far left] at the cross product of two sine waves, and the Grasshopper definition that created these simulated harmonograph drawings is simply an extension of this principle. The decay rate is set as an adjustable constant. The following equation is the basis for this Grasshopper definition, which simulates a two pendulum harmonograph producing a 2D output. X = sin(at)*(1-kt) Y = sin(b(t+d))*(1-kt) t = time [s] a = X frequency [Hz] b = Y frequency [Hz] d = Y phase displacement [s] k = decay [fraction/cycle]
1
2
3
4
Adjustable sliders control frequency, phase and decay
1. Harmonograph produced where harmonic ratio is nearly 1:1 2. Lissajous Curves made from non decaying sine waves at different harmonies 3. Simulated two pendulum 2D harmonographs created using Grasshopper definition - images created using different harmonies 4. Grasshopper definition used to create the above harmonographs
Performs the required mathematical function on a series of numbers to be used as X, Y co-ordinates
Plots points according to X,Y functions, and interpolates these into a smooth curve