The logistic map connects fluid convection, neuron firing, the Mandelbrot set and so much more. Fasthosts Techie Test competition is now closed! Learn more about Fasthosts here: https://www.fasthosts.co.uk/veritasium Code for interactives is available below... Animations, coding, interactives in this video by Jonny Hyman 🙌 Try the code yourself: https://github.com/jonnyhyman/Chaos References: James Gleick, Chaos Steven Strogatz, Nonlinear Dynamics and Chaos May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976). https://doi.org/10.1038/261459a0 Robert Shaw, The Dripping Faucet as a Model Chaotic System https://archive.org/details/ShawRobertDrippingFaucetAsAModelChaoticSystem1984_201811/mode/2up Crevier DW, Meister M. Synchronous period-doubling in flicker vision of salamander and man. J Neurophysiol. 1998 Apr;79(4):1869-78. Bing Jia, Huaguang Gu, Li Li, Xiaoyan Zhao. Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns Cogn Neurodyn (2012) 6:89–106 DOI 10.1007/s11571-011-9184-7 A Garfinkel, ML Spano, WL Ditto, JN Weiss. Controlling cardiac chaos Science 28 Aug 1992: Vol. 257, Issue 5074, pp. 1230-1235 DOI: 10.1126/science.1519060 R. M. May, D. M. G. Wishart, J. Bray and R. L. Smith Chaos and the Dynamics of Biological Populations Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 413, No. 1844, Dynamical Chaos (Sep. 8, 1987), pp. 27-44 Chialvo, D., Gilmour Jr, R. & Jalife, J. Low dimensional chaos in cardiac tissue. Nature 343, 653–657 (1990). https://doi.org/10.1038/343653a0 Xujun Ye, Kenshi Sakai. A new modified resource budget model for nonlinear dynamics in citrus production. Chaos, Solitons and Fractals 87 (2016) 51–60 Libchaber, A. & Laroche, C. & Fauve, Stephan. (1982). Period doubling cascade in mercury, a quantitative measurement. http://dx.doi.org/10.1051/jphyslet:01982004307021100. 43. 10.1051/jphyslet:01982004307021100. Special thanks to Patreon Supporters: Alfred Wallace, Arjun Chakroborty, Bryan Baker, DALE HORNE, Donal Botkin, halyoav, James Knight, Jasper Xin, Joar Wandborg, Lee Redden, Lyvann Ferrusca, Michael Krugman, Pindex, Ron Neal, Sam Lutfi, Tige Thorman, Vincent Special thanks to: Henry Reich for feedback on earlier versions of this video Raquel Nuno for enduring many earlier iterations (including parts she filmed that were replaced) Dianna Cowern for title suggestions and saying earlier versions weren't good Heather Zinn Brooks for feedback on an earlier version. Music from: https://epidemicsound.com "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4" https://ve42.co/Artlist "Busy World" "Children of Mystery"

Thank you to Wondrium for sponsoring today's video! Signup for your FREE trial to Wondrium here: http://ow.ly/aJUh50LnlQP -------------------------------- If you like this video, check out writer Geraint Lewis´ excellent book, co-written with Chris Ferrie: Where Did the Universe Come From? And Other Cosmic Questions: Our Universe, from the Quantum to the Cosmos https://www.amazon.com/Where-Universe-Other-Cosmic-Questions/dp/1728238811 AND check out his Youtube channel: https://www.youtube.com/c/AlasLewisAndBarnes Incredible thumbnail art by Ettore Mazza, the GOAT: https://www.instagram.com/ettore.mazza/?hl=en Animations by the superb Jero Squartini https://www.fiverr.com/share/0v7Kjv using Manim - MIT License, (c) 2020-2023 3Blue1Brown LLC Art created by soso112429 Music from Silver Maple, Epidemic Sound and Artlist. Stock footage from Videoblocks and Artgrid, images of galaxies from NASA and ESO/Hubble. Image Credits: Tsung Dao Lee (left) and Chen Ning Yang at a blackboard in an Institute office from the Shelby White and Leon Levy Archives Center. Cobalt 60 By V1adis1av - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=95281927 00:00 Introduction 04:21 Symmetry is Everywhere 10:46 The Hidden Rules Of The Universe 22:36 How To Break The Universe 34:52 Why Did The Universe Freeze?

Dr. Robert Gilbert shares his teachings on Sacred Geometry and the divine designs which manifest everything in material existence, and offers practical methods for raising awareness to utilize and evolve consciousness on individual and global levels. I welcome you to an exclusive presentation on my channel, presented to you by Gaia, called: (Sacred Geometry: Spiritual Science) with Dr. Robert J. Gilbert. Special offer from Gaia, exclusive to all of my subscribers 🎁 ◉ Visit my Gaia Portal by clicking the link in the description area or pinned to the comment section below. You can watch Free videos and join with a special 7-day FREE Trial. 👉 at https://www.gaia.com/garylite Links to the series pages: Series Page – Sacred Geometry: https://gaia.com/glite_sg Gaia Home: https://bit.ly/glite_gaia Gaia TV Series: https://bit.ly/glite_TV Gaia Films: https://bit.ly/glite_films @GaiaVideo HELP SUPPORT MY WORK 💗🙏💗 If you wish to make a small Donation click on the link below: Thank you ◉ PayPal Donation Link: https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=6QHHNJVALEQDN ◉ My Websites: http://garylite.com/ #gaiatv #gaia #garylite

Twenty-three centuries ago Archimedes showed how complicated physical phenomena, such as his Law of Buoyancy, can arise from a few basic assumptions. His seminal work has led to attempts to explain the entire cosmos from a few elementary physical principles. This talk will trace the history of this quest for a Theory of Everything and describe some of the unexpected roadblocks it has encountered in the 21st century. Chris Rorres, Ph.D. is Professor Emeritus of Mathematics at Drexel University and Lecturer of Epidemiology at the University of Pennsylvania. Dr. Rorres has appeared in many documentaries explaining Archimedes¹ discoveries, inventions, and continuing influence. His web site on Archimedes, established in 1995, is visited by hundreds of thousands of students and scholars each year.

PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateOKAY ↓ More info and sources below ↓ We’re on PATREON! Join the community ►► https://www.patreon.com/itsokaytobesmart SUBSCRIBE so you don’t miss a video! ►► http://bit.ly/iotbs_sub ↓↓↓ More info and sources below ↓↓↓ The golden ratio. Some say it’s the most mythical number in the universe. Others say it underlies everything from nature’s patterns to beauty in art and design. But, like, what is it? And does the myth of the golden ratio hold up to its mathematical reality? Let’s find out References: https://sites.google.com/view/golden-ratio-references/home ----------- Special thanks to our Brain Trust Patrons: Roy Lasris Javier Soto dani bowman David Johnston Ahmed Elkhanany Zenimal Salih Arslan Baerbel Winkler Robert Young Amy Sowada Benjamin Teinby Eric Meer Jay Stephens Peter Ehrnstrom Dustin Marcus Tuepker Karen Haskell AlecZero Diego Lombeida Join us on Patreon! https://patreon.com/itsokaytobesmart Twitter http://www.twitter.com/DrJoeHanson http://www.twitter.com/okaytobesmart Instagram http://www.instagram.com/DrJoeHanson http://www.instagram.com/okaytobesmart Merch https://store.dftba.com/collections/its-okay-to-be-smart Facebook https://www.facebook.com/itsokaytobesmartpbs/

Get Exclusive Alternative Healing Bonuses with a Gaia Annual Plan - https://bit.ly/3FoIQaO How do divine patterns of creation define what manifests on every level of physical reality? Founder of the Vesica Institute for Holistic Studies Robert J. Gilbert, Ph.D., offers his 40 years of insight into mystical truths, exploring four of the most profound secrets of Sacred Geometry. Sharing his expertise about the patterns which manifest everything in material existence, Dr. Gilbert offers practical methods for raising awareness to utilize Sacred Geometry and evolve consciousness on individual and planetary levels. About Gaia: Gaia offers the largest resource of consciousness expanding videos. Answer life's deeper questions and go beyond the mainstream narrative with Gaia— a member-supported media network of truth seekers and believers empowering an evolution of consciousness. Explore over 8,000 ad-free, streaming titles that challenge modern paradigms and allow you to manifest the reality that defines your being. You can experience Gaia in English, Spanish, German, or French. We offer original, dubbed or subtitled content in these languages. Join hundreds of thousands of members in 185 countries in awakening your consciousness. Connect with Gaia: Visit Gaia WEBSITE: https://www.gaia.com/ Like Gaia on FACEBOOK: https://www.facebook.com/Gaia Like Gaia Unexplained on FACEBOOK: https://www.facebook.com/GaiaUnexplained Like Gaia Yoga on FACEBOOK: https://www.facebook.com/yogaongaia Follow Gaia on YOUTUBE: https://www.youtube.com/c/GaiaVideo Follow Gaia on TWITTER: https://twitter.com/yourmothergaia Follow Gaia on INSTAGRAM: https://www.instagram.com/wearegaia/ Follow Gaia Yoga on INSTAGRAM: https://www.instagram.com/yogaongaia/ #Gaia

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Today, a long overdue foray into the realm of VORTEX MATHEMATICS :) 00:00 Intro 04:16 The vortex 08:10 The maths of remainders and digital roots 13:25 Demystifying the vortex 16:30 A matter of base. The 8 fingered Tesla. 19:21 Explanation why the digital root is the remainder on division by 9 24:01 Tristan's challenge 24:44 The magic of modular multiplication maths 25:19 Intuition for multiplier - 1 petals 28:23 Thank You! Coding competition: My wish list for the modular times table diagram app: -Being able to color line segments according to length. -Indication of the "direction" of multiplication. 1x2 = 2 and so there should really be a little arrow from 1 to 2 not just a simple connection :) -different loops in different colors. ... Here is the prize, a copy of my and Marty's new book. https://bookstore.ams.org/mbk-141/ That early Mathologer video featuring the modular times tables Times Tables, Mandelbrot and the Heart of Mathematics https://youtu.be/qhbuKbxJsk8 A really nice article about various ways to generate the cardioid by Dave Richeson https://divisbyzero.com/2018/04/02/i-heart-cardioids/ Nice debunking/demystifying article about vortex math by "Professor Puzzler" https://www.theproblemsite.com/vortex/ For a growing pile of implementation of modular times table diagrams see my comment pinned to the top of the comment section of this video. Simon Plouffe's website http://plouffe.fr/Simon%20Plouffe.htm Articles by him relevant to this video can be found in this directory http://plouffe.fr/Inverseofprimes/ See in particular the files The shape of b^n mod p.pdf La forme de bn mod p.pdf What I am talking about in this video is really just the tip of a bizarre mathematical iceberg that most mathematically minded people are completely unaware of. Have a look at this presentation by Marko Rodin on vortex math (beware serious nutty and at the same time truely beautifully presented numerology ahead :) A LOT more than is usually reported on in popular YouTube videos. https://sciencetosagemagazine.com/vbm-vortex-based-mathematics-with-marko-rodin/ In turn this iceberg is just another tip of an even bigger iceberg of mainly wishful thinking. Have a look: https://sciencetosagemagazine.com/category/library/ Today's music: Aftershocks by Ardie Son Enjoy! Burkard