Fractal Art Gallery

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 which is way quicker then it takes to compare car insurance.

 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

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