How they played chess forever, snowflakes, and other ubiquitous joys of avoiding an awawa in binary

How they played chess forever, snowflakes, and other ubiquitous joys of avoiding an awawa in binary: The Prouhet-Thue-Morse Sequence and its properties (a math video essay)

00:00:00 Intro
00:00:24 CH1 Let's play chess (forever) Part 1
00:02:55 CH2 Counting in the Fjords
00:05:15 CH3 "0", "1" and "01"
00:08:50 CH4 Thue's Answer and The Prouhet-Thue-Morse Sequence
00:12:57 CH5 (Part1) An awawa and other preliminaries
00:19:37 CH5 (Part2) Proof that the Prouhet-Thue-Morse Sequence avoids an awawa
00:27:23 CH6 Cube Free and Other Corollaries
00:30:32 CH7 Eugene Prouhet
00:38:14 CH8 H.C. Marston Morse
00:45:13 CH9 Flip The Bit
00:50:36 CH10 Substitutions and Snowflakes
00:58:46 CH11 Let's play chess (forever) Part 2
01:00:43 Extras and Wrap-Up

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Sources:
Allouche, Jean-Paul, and Jeffrey Shallit. “The Ubiquitous Prouhet-Thue-Morse Sequence.” In *Sequences and Their Applications*, edited by C. Ding, T. Helleseth, and H. Niederreiter, 1–16. London: Springer London, 1999. https://doi.org/10.1007/978-1-4471-05...

Euwe, M. “Mengentheoretische Betrachtungen ̈ uber das Schachspiel.” Proc. Konin. Akad. Wetenschappen, Amsterdam 32 (1929), 633–642.

Hanging Pawns, Rook and Bishop vs Rook Endgame    • Rook and Bishop vs Rook Endgame  

Holdener, J. and Ma, J. “WHEN THUE-MORSE MEETS KOCH.” Fractals 13, no. 03 (September 2005): 191–206. https://doi.org/10.1142/S0218348X0500....

Holdener, MoMath Math encounters “Immersion: Using Digital Art to Make Surprising Connections”:    • Math Encounters -- Judy Holdener - Im...  

MAA Euler Correspondence archive: http://eulerarchive.maa.org/correspon...

Morse, Harold Marston. “A One-to-One Representation of Geodesics on a Surface of Negative Curvature.” American Journal of Mathematics 43, no. 1 (1921): 33–51. https://doi.org/10.2307/2370306.

———. “Recurrent Geodesics on a Surface of Negative Curvature.” Transactions of the American Mathematical Society 22, no. 1 (1921): 84–100. https://doi.org/10.1090/S0002-9947-19....

Prouhet, E. “Mémoire Sur Quelques Formules Générales d’analyse.” Journal de Mathématiques Pures et Appliquées 1 (1856): 321–44. http://www.numdam.org/item/?id=JMPA_1...

Rozendorn, E. R. “Surfaces of Negative Curvature.” In *Geometry III: Theory of Surfaces*, edited by Yu. D. Burago and V. A. Zalgaller, 87–178. Encyclopaedia of Mathematical Sciences. Berlin, Heidelberg: Springer, 1992. https://doi.org/10.1007/978-3-662-027....

Séébold, Patrice. “Sequences Generated by Infinitely Iterated Morphisms.” Discrete Applied Mathematics 11, no. 3 (July 1, 1985): 255–64. (https://doi.org/10.1016/0166-218X(85)....

Venkitachalam, Mahesh ****“Koch Snowflake and the Thue-Morse Sequence · Electronut.” Accessed October 9, 2023. https://electronut.in/koch-snowflake-....

Williamson, Christopher. “An Overview of the Thue-Morse Sequence,” (2012) https://sites.math.washington.edu/~mo...

Thue, Axel “Uber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen”, ¨ Norske vid. Selsk. Skr.
Mat. Nat. Kl. 1 (1912), 1-67. Reprinted in ”Selected mathematical papers of Axel Thue,” T. Nagell,
ed., Universitetsforlaget, Oslo, 1977, 413-478.

Threefold Position rule in chess: [https://www.chess.com/terms/threefold... threefold repetition rule states,player can claim a draw]

Zukertort vs Steinitz 1886 match history and data: https://www.chessgames.com/perl/chess...

Zukertort vs Steinitz 1886 match preliminaries https://www.chessarch.com/archive/188...

Sourced Images:

Klein quartic with closed geodesics https://commons.wikimedia.org/wiki/Fi... made avaliaible under CC ****Attribution-ShareAlike 4.0 International https://creativecommons.org/licenses/...

Koch Snowflake: https://personal.math.ubc.ca/~cass/co...

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