(Originally posted at http://joelnoche.multiply.com/journal/item/53/Thue-Morse-Sequence on May 17, 2011 10:43 AM)
My undergraduate and master’s degrees are in electrical engineering. Although my master’s thesis was on computer arithmetic and asynchronous circuits, I was also interested in pseudo-random number generators.
On March 29, 2004, I was thinking of how to simply generate an infinite non-periodic binary sequence. I came up with the sequence obtained by starting with 0 then, at each succeeding step, replacing each 0 with 01 and each 1 with 10.
Because I had no formal training in pure mathematics or in theoretical computer science, I had never seen this sequence before and thought that I was the first to discover it. But after reading my copy of Wolfram’s A New Kind of Science, I realized that I had stumbled onto the Thue-Morse Sequence. Thus began my adventures with the field of study known as Combinatorics on Words…