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Wayne, I don't recognize that specific pattern, but it looks like a variant of the Hilbert space-filling curve:

Here are pictures of a huge number of different fractal curves (i.e. continuous patterns of lines that, in the limit, have a Hausdorff dimension that exceeds 1. The Hilbert curve has Hausdorff dimension 2.0. Some of them resemble your pattern, but I didn't see any exact match.


P.S. I recently wrote a post for the "other" Math board, on the subject of Vladimir Arnold, the Russian mathematician.
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