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In a way the two are related.Tim, I noticed the radiation symbol in the center. Wonder if they are connected some how? Meaning the natives that used the pattern and the symbol chosen.
Many native American designs use a center point with the design radiating out from it. These center of these designs represent various things, birth, seeds, mother earth, etc that all signify a starting point and growth from that point. Sometimes the symbolism represented the physical growth (squash blossom), or the personal and spiritual growth of a person on their journey through life. There are many other meanings, and I'm sure there are a few thesis that have been or could be written on the topic. Many native American designs also use an odd rather than even number of elements in the design. Three elements radiating from a central point is the "base level" so to speak.
The radiation symbol was developed (doodled) by a small group at UC-Berkley in 1946. They were looking for a symbol to represent radiation. They had several motifs, but picked the current one which symbolized "activity" radiating from an atom.
The similarity is obvious, but I don't know if that is coincidence, or if the first person to doodle the design may have been influenced by Native American designs they had seen sometime in the past.
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