Quasi-Crystal III

NOTE: MUST CREDIT THE IMAGES AND NOTIFY ERIC J. HELLER WHEN AND WHERE THE IMAGES ARE USED

Illustration: Quasicrystal III

Caption: An addition of 9 plane waves equally spaced in angle, The plane waves were "pivoted" about the center of the "sun", giving an approximation to a Bessel function centered there, which breaks down outside a radius which is already inside the sun region. The region of breakdown is most of the image. The slice shown in lighter colors is one repeating unit which if copied 8 times would regenerate the whole image. This image is a quasicrystal as well, except that the approximate repetitions of the sun region are very farther away from each other than in Quasicrystal II, which has 5 waves added together, but not so far away as in Comet, which has 21 waves. All additions of more than three plane waves are quasicrystals, but the near-repetition distance moves out rapidly as the number of plane waves used increases. What you call a "near-repetition" is somewhat arbitrary. The more exact one makes the repetition requirement, the further away the repetitions become. There are no really good repetitions in the image, although there are many poor ones.

Credit: © Eric J. Heller, Harvard University
Website: http://www.ericjhellergallery.com/index.pl?page=image;iid=39
NSF Funded: Yes Research supported by Harvard's NSEC (NSF) grant
NSF Permission to Use: Yes Internal and External
Original File Name: quasicrystal_iii.jpg
In Image Library: No
Permission Form: PF0019.pdf

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