Fractal Art Gallery
Spherical Harmonics
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Fractal Art Gallery Spherical Harmonics |
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.
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
| For
a technical discussion of spherical harmonics, complete with equations,
please go to the University of Oviedo, Spain's department of physical
and analytical chemistry: HERE. |
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.
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