This is an interactive web page (based on Javascript) to visualize Spherical Harmonics.
You can directly select the indices 'l' and 'm' or start an animation
('show all m' loops 'm' for fixed 'l' by 'm = 0,...,l' and
'show 20 l' loops 'l' for fixed 'm' by 'l = m,...,m+20')
All other options 'back', 'rotate', 'export', 'extras',... are explained below the image.

The image shows one specific surface spherical harmonic of degree 'l' and order 'm',
denoted as 'Y_{lm}(φ,λ)'
(they are solutions of ΔY_{lm} = 0).
Any source-free field on the sphere can be computed with these terms as the double sum over
'l' (l = 1,..,l_{max}) and 'm' (m = 0,..,l) with:

where 'φ' = [-90°,+90°] is the latitude, 'λ' = [0°,360°] the longitude.
'P_{lm}(x)' are the Legendre polynoms and
'C_{lm}', 'S_{lm}' are constant coefficients, which describe the actual field/model.
Here the cos-term 'C_{lm}P_{lm}(sin(φ))cos(m λ)'
is displayed, arbitrarily scaled by C_{lm} = 100⁄sqrt(l).
The sin-term is
identical with a phase shift of π⁄m.
The blue lines indicate the zero-circles, where 'Y_{lm} = 0'.

^{1} extracted from:
Ilk, K.H., J. Flury, R. Rummel, P. Schwintzer, W. Bosch, C. Haas, J. Schröter, D. Stammer,
W. Zahel, H. Miller, R. Dietrich, P. Huybrechts, H. Schmeling, D. Wolf, J. Riegger,
A. Bardossy, A. Güntner, 2004:
Mass Transport and Mass Distribution in the Earth System (PDF) --
Contribution of the New Generation of Satellite Gravity and Altimetry Missions to
Geosciences, Proposal for a German Priority Research Program