most recent 30 from http://mathoverflow.net 2013-05-26T08:41:22Z http://mathoverflow.net/feeds/user/21533 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/88773/branches-of-the-fibonacci-word-tree/88901#88901 Nathaniel Shar 2012-02-19T06:39:33Z 2012-02-19T19:26:18Z

<p>The answer to the question "Is there any regularity to the location of the branches?" appears to be yes. Here is <a href="http://math.rutgers.edu/~nbs48/fibonacci-word-tree/fib500.png" rel="nofollow">a diagram of the first 500 branches</a> (a black pixel denotes a branch, and a white pixel denotes no branch, with the root in the upper-left-hand corner just like in your diagram). The regularity is apparent. You might need to zoom in if the pixels are too small.</p> <p>Of course, I say "appears to be" because I haven't yet proved that the pattern continues, or even described precisely what the pattern is.</p> <p><img src="http://math.rutgers.edu/~nbs48/fibonacci-word-tree/fib500.png" width="300"/></p> <p>P.S.: I would have left this as a comment, since I doubt it qualifies as a full "answer", but apparently I need more reputation to do that. My apologies.</p>