(Originally posted at http://joelnoche.multiply.com/journal/item/54/Stewarts-Choral-Sequence on May 18, 2011 1:01 AM)
On February 27, 2008, I started to study cube-free infinite binary words—infinitely long words using two letters that never repeat a pattern three times in a row. So, for example, the finite word 11101010 is not cube-free because its first three letters are a cube and its last six letters are a cube. The word 01101001 is cube-free.
The first infinite cube-free word on page 1 of my notes (shown on the left) is also known as Reverend Back’s abbey floor. (Click on the picture to see more detail.) Note that the Thue-Morse sequence (which I talked about in a previous blog entry) is also cube-free.
The last sequence on the page is also cube-free and is known as Stewart’s choral sequence. A few months later I wrote a paper about it which I presented at the 2008 Mathematical Society of the Philippines annual convention. It was published in Gibón in 2008.