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. The Mandelbrot set is a perfect example of how a simple mathematical rule can produce incredible complexity.
This video explains how the Mandelbrot set is constructed by iterating a quadratic function on the complex plane. It also delves into the connection between Mandelbrot sets and Julia sets as well as the mechanics of how they work.
We also retrace the history of the discovery and exploration of these important sets. Today mathematicians working in the field of complex dynamical systems are patiently unraveling the set's mysteries and may be on the verge of solving the Mandelbrot Locally Connected conjecture, which would allow them to describe the set completely.
Read the full article: https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/
Specials thanks for providing Mandelbrot Set visuals:
Maths.town https://www.youtube.com/@MathsTown
Movie Vertigo https://www.youtube.com/@MovieVertigo
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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