The Mandelbrot set is a special shape, with a fractal outline. Use a computer to zoom in on the set’s jagged boundary and no matter how deep you explore, you’ll always see near-copies of the original set — an infinite, dizzying cascade of self-similarity and novel features. The Mandelbrot set is a perfect example of how a simple mathematical rule can produce incredible complexity. This video covers how the Mandelbrot set is constructed by iterating a quadratic function on the complex plane. It also delves into the connections between Mandelbrot and Julia sets while explaining the mechanics of how they both work. We also retrace the history of the discovery and exploration of these important sets, including current research on solving the key Mandelbrot Locally Connected conjecture (MLC). Read the full article: https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/ ---------- Specials thanks for their Mandelbrot Set visualizations: Maths.town null Movie Vertigo null Dynamic Maths https://www.dynamicmath.xyz/mandelbrot-julia/ Fractally https://luckgrib.com/fractally/ ---------- Recommend in-depth videos about the Mandelbrot set: What's so special about the Mandelbrot Set? - Numberphile https://www.youtube.com/watch?v=FFftmWSzgmk The Mandelbrot Set - Numberphile: https://www.youtube.com/watch?v=NGMRB4O922I Beyond the Mandelbrot set, an intro to holomorphic dynamics - 3Blue1Brown: https://www.youtube.com/watch?v=LqbZpur38nw ---------- Chapters: 00:00 What is the Mandelbrot set? 00:58 How an iterated quadratic function defines the Mandelbrot set 01:30 The field of complex dynamical systems 01:54 Julia sets explained 04:06 The discovery of the Mandelbrot set 05:03 Constructing Mandelbrot sets vs Julia sets 05:53 Why mathematicians study the boundary regions 06:22 Mandelbrot Locally Connected conjecture, MLC ---------- - VISIT our website: https://www.quantamagazine.org/ - LIKE us on Facebook: https://www.facebook.com/QuantaNews - FOLLOW us Twitter: https://twitter.com/QuantaMagazine Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/