DecodingThe Mandelbrot Set, Math’s Famed Fractal
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-qu...
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Specials thanks for their Mandelbrot Set visualizations:
Maths.town / @mathstown
Movie Vertigo / @movievertigo
Dynamic Maths https://www.dynamicmath.xyz/mandelbro...
Fractally https://luckgrib.com/fractally/
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Recommend in-depth videos about the Mandelbrot set:
- What's so special about the Mandelbrot Set? - Numberphile • What's so special about the Mandelbro...
- The Mandelbrot Set - Numberphile: • The Mandelbrot Set - Numberphile
- Beyond the Mandelbrot set, an intro to holomorphic dynamics - 3Blue1Brown: • Beyond the Mandelbrot set, an intro t...
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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
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