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Spherical Harmonics

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Here is a long series, a study if you will, on nineteen separate pages,
of over 640 three-dimensional visualizations (in spherical coordinates
rho, theta, and phi) of equations of the form:

rho = sin(a * phi)^b + cos(c * phi)^d +  
  + sin(e * theta)^f + cos(g * theta)^h

The captions underneath each image on the nineteen gallery pages
listed below correspond to the variables a thru h in the above equation.
Each page will take about 20 seconds to load the thirty-six images at
56 kb download speed -- modern speeds are much quicker.

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 Images 1-36  Images 181-216  Images 361-396  Images 517-552
 Images 37-72  Images 217-252  Images 397-408  Images 553-588
 Images 73-108  Images 253-288  Images 409-444  Images 589-624
 Images 109-144  Images 289-324  Images 445-480  Images 625-643
 Images 145-180  Images 325-360  Images 481-516   

 

 

 

 

 

 

The first twelve pages, images 1-408, contain coefficients of four or less,
while images 409-643 contain coefficients up to eight.

Spherical Harmonics Page 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / Index

Further research may be done at the chemistry department of the University of Regensburg in Germany. If you're interested, go HERE.
Additional information with pictures and links is available at Mathworld: HERE.