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How does order spontaneously arise out of chaos? This video is sponsored by Kiwico — go to for 50% off your first month of any crate. An enormous thanks to Prof. Steven Strogatz — this video would not have been possible without him. Much of the script-writing was inspired and informed by his wonderful book Sync, and his 2004 TED talk. He is a giant in this field, and has literally written the book on chaos, complexity, and synchronization. It was hard to find a paper in this field that Steven (or one of his students) didn't contribute to. His Podcast “The Joy of X“ is wonderful — please listen and subscribe wherever you get your podcasts Nicky Case's Amazing Firefly Interactive — Great Kuramoto Model Interactive — References: Strogatz, S. H. (2012). Sync: How order emerges from chaos in the universe, nature, and daily life. Hachette UK. — Strogatz, S. H. (2000). From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D: Nonlinear Phenomena, 143(1-4), 1-20. — Goldsztein, G. H., Nadeau, A. N., & Strogatz, S. H. (2021). Synchronization of clocks and metronomes: A perturbation analysis based on multiple timescales. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(2), 023109. — The Broughton Suspension Bridge and the Resonance Disaster — Bennett, M., Schatz, M. F., Rockwood, H., & Wiesenfeld, K. (2002). Huygens's clocks. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458(2019), 563-579. — Pantaleone, J. (2002). Synchronization of metronomes. American Journal of Physics, 70(10), 992-1000. — Kuramoto, Y. (1975). Self-entrainment of a population of coupled non-linear oscillators. In International symposium on mathematical problems in theoretical physics (pp. 420-422). Springer, Berlin, Heidelberg. -- Great video by Minute Earth about Tidal Locking and the Moon — Strogatz, S. H., Abrams, D. M., McRobie, A., Eckhardt, B., & Ott, E. (2005). Crowd synchrony on the Millennium Bridge. Nature, 438(7064), 43-44. — Zhabotinsky, A. M. (2007). Belousov-zhabotinsky reaction. Scholarpedia, 2(9), 1435. — Flavio H Fenton et al. (2008) Cardiac arrhythmia. Scholarpedia, 3(7):1665. — Cherry, E. M., & Fenton, F. H. (2008). Visualization of spiral and scroll waves in simulated and experimental cardiac tissue. New Journal of Physics, 10(12), 125016. — Tyson, J. J. (1994). What everyone should know about the Belousov-Zhabotinsky reaction. In Frontiers in mathematical biology (pp. 569-587). Springer, Berlin, Heidelberg. — Winfree, A. T. (2001). The geometry of biological time (Vol. 12). Springer Science & Business Media. — The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version ) [Computer software]. Special thanks to Patreon supporters: Mac Malkawi, Oleksii Leonov, Michael Schneider, Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Lyvann Ferrusca, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal Written by Derek Muller and Petr Lebedev Animation by Fabio Albertelli and Jakub Misiek Simulations and 3D Animation by Jonny Hyman Filmed by Derek Muller and Raquel Nuno Edited by Derek Muller Additional video supplied by Getty Images Thumbnail by Ignat Berbeci More footage from NASA's Scientific Visualization Studio 100 metronome video from Intro animation by Jorge Cham Thanks for the BZ footage from SteinbockGroup: and NileRed Animation of waves in the heart from The Virtual Heart/ EM Cherry/ FH Fenton — and Chemical materials and protocol provided by Mike Morris and the UCI Chemistry Outreach Program ~jsnowick/outreach/UCI_Outreach/ Thanks to Alie Ward for title/thumbnail consultation Thanks to Dr Juliette Becker and Dr James O'Donoghue for the planetary science help Music from Jonny Hyman, Epidemic Sound “Seaweed“ “Deeper Than The Ocean“ “Ripple Effect“ Music also from Artlist “Children of Mystery“ Thumbnail by Ignat Berbeci
