A very good point to start would surely be: Allouche/Shallit: "The Ubiquitous Prouhet-Thue-Morse Sequence" (URL: https://cs.uwaterloo.ca/~shallit/papers.html ) Also their book "Automatic Sequences". The paper mentions a property that I find very striking, the connection to the Prouhet-Tarry-Escott problem (see section 5.1). Best regards, jj * James Propp <jamespropp@gmail.com> [Jan 09. 2017 08:43]:
Do any of you have any favorite private facts about the Thue-Morse sequence, or any favorite links to existing content on this subject?
(I already know about the Numberphile video "The Fairest Sharing Sequence Ever".)
I'd especially like a link to an image or animation graphically depicting the self-similarity of the Thue-Morse sequence. (I have my own ideas for a GIF that would depict this, but I prefer not to create things that already exist.)
I'd also be interested in knowing whether any well-known (or not so well-known) poems use an abbabaab rhyme scheme, or whether there is any interesting music based on the Thue-Morse sequence.
(Yes, this is all for my next Mathematical Enchantments piece.)
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun