Unveiling the Hidden Connection Between the Logistic Map and the Mandelbrot Set 🔍

Hi all, this video is my entry for Summer of Math Exposition 3. References: Veritasium Video: https://youtu.be/ovJcsL7vyrk?si=WhhnFleCEU5JvHFN 3D Bifurcation Gif: https://github.com/jonnyhyman/Chaos Logistic Map: https://mathworld.wolfram.com/LogisticMap.html Feigenbaum Constant: https://youtu.be/ETrYE4MdoLQ?si=aeA_8nwURqALdr6C https://mathworld.wolfram.com/FeigenbaumConstant.html Further Reading on when the Feigenbaum Constant applies: https://mathworld.wolfram.com/SchwarzianDerivative.html https://demonstrations.wolfram.com/TheSchwarzianDerivativeOfIteratedFunctions/ Corrections: The tent map is x•min(x,1-x), not x•min(x,x-1) Another great video exploring the relationship between the Mandelbrot Set & the logistic map: https://youtu.be/TPYvmSMdDWQ Chapters: 0:00 Intro 00:31 Bifurcation Diagram 02:20 Mandelbrot Set 04:52 3D Bifurcation Gif 05:14 Building a 3D Bifurcation Diagram 07:48 Recap 08:45 Logistic Map Fractal 09:32 Logistic Map 3D Bifurcation Diagram 10:09 Feigenbaum Constant 12:00 Outro