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

m0
m1
m2
m3
m4
m5
m6
m7
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(m0θ)m1+cos(m2θ)m3+sin(m4ϕ)m5+cos(m6ϕ)m7

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:



 

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