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Thue-Morse rings by markdow Thue-Morse rings by markdow
Each sequential generation of the Thue-Morse sequence in concentric rings, starting at the horizontal. The first generation is at the center.

The black and white patterns are identical after a half turn about the center. It is a binary fractal.

"But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius." Marston Morse

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This image is dedicated to the Public Domain. There are no restrictions on use. Claiming to be the originator or owner, explicitly or implicitly, is bad karma. A link (if appropriate), a note to markdow30@gmail.com, and credit are appreciated but not required.
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:iconsakurasoul:
sakurasoul Featured By Owner Jan 25, 2010  Student Interface Designer
Aaaah, my eyes hurt when they go inside.
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:iconhop41:
Hop41 Featured By Owner Jul 18, 2009
You've done a lot of stuff based on Thue-Morse. This is one of the more visually interesting experiments.
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:iconsilverb:
silverb Featured By Owner Jul 18, 2009
:salute:
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:iconhotmetal53:
hotmetal53 Featured By Owner Jul 12, 2009
This kind of reminds me of Walsh waves or functions.
--
Allen Brown [link]
The rub is finding that balance between being open-minded enough to accept radical new ideas but not so open-minded that your brains fall out. --- Michael Shermer
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:iconmarkdow:
markdow Featured By Owner Jul 13, 2009
Yes, they are related. In some orderings of Walsh functions (natural or Hadamard) these Thue-Morse words occur at indices that are integer ratios of powers of two. They are a special subset of the Walsh functions.
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:iconhotmetal53:
hotmetal53 Featured By Owner Jul 13, 2009
It's rare to find someone who has even heard of Walsh functions. In the 70s I had thought to do electronic synthesis with them. But I never got around to it. And I hadn't heard of them since then.
--
Allen Brown [link]
Since light travels faster than sound, some people appear to be bright until you hear them speak. --– Brian Williams
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:iconmarkdow:
markdow Featured By Owner Jul 13, 2009
There's some self-interested selection here. I thought it was rare to find someone who wondered if all logic gates could be formed from XOR2! We both have a deep geek streak.
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:iconhotmetal53:
hotmetal53 Featured By Owner Jul 15, 2009
:nod:
--
Allen Brown [link]
An island of stability. -- President Jimmy Carter (1979) describing the Shah of Iran. The Shah was overthrown a few months later.
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July 12, 2009
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