This collection of eight rope-textured knots is a selection of interesting patterns formed by Lissajous equations.

Lissajous curves are complex, three-dimensional curves created by the interaction of three perpendicular simple harmonic motions or sine waves. This selection includes only non-intersecting curves.

At first the curves can appear chaotic but when viewed from specific perspectives they demonstrate highly symmetrical patterns.

Files are named according to the parametric inputs for the equation. The first three numbers indicate the number of waves in the x,y and z directions respectively. The second series of characters indicate the phase shift of each of the x,y and z waveforms. “0” indicates the waveform is not shifted. “P” indicates that the waveform has been shifted by pi/2.

These files are intended for resin printing but could be possible with FDM printing if scaled up and properly supported.