The pseudo-spherical harmonics of Paul Bourke with θ and φ interchanged:

Click button to open the graphic in a separate full window. The figure can be rotated by clicking and dragging with a mouse or swiping on a touch device, as well as zoomed in or out with a mouse wheel or pinching on a touch device.

The surface is defined parametrically by

\[ r = \sin( m_0 \theta )^{m_1} + \cos( m_2 \theta )^{m_3} + \sin( m_4 \phi )^{m_5} + \cos( m_6 \phi )^{m_7} \]

The eight integer parameters are randomized on page load. The inputs are arranged as a two-column matrix for a more compact interactive graphic.

Also available are visualizations of proper spherical harmonics using Math.

Complete code for this example:


Examples Page