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

When I first saw the comparison between the Mandelbrot set and the Logistic map, I was fascinated and it motivated me to investigate the “not so obvious” but necessary relationship between the Mandelbrot set and the Logistic map.


#mandelbrot #logistic #bifurcation

Some of the math animations used in this video was created using Manim - https://www.manim.community/


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References:
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A Population of Rabbits and the Mandelbrot Set - https://tomrocksmaths.files.wordpress.com/2022/05/maths-essay-2.0.pdf
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Beyond the Mandelbrot set, an intro to holomorphic dynamics (3Blue1Brown - Youtube) - https://www.youtube.com/watch?v=LqbZpur38nw&t
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Logistic map (Wikipedia) - https://en.wikipedia.org/wiki/Logistic_map
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Mandelbrot-bifurcation (GeoGebra) - https://www.geogebra.org/m/m8kd5bvb
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Mandelbrot set (Wikipedia) - https://en.wikipedia.org/wiki/Mandelbrot_set
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The boundary of the logistic map - https://blbadger.github.io/logistic-boundary.html
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The Mandelbrot Set (Numberphile - Youtube) - https://www.youtube.com/watch?v=NGMRB4O922I
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The Mandelbrot Set and Julia Sets - https://users.math.yale.edu/public_html/People/frame/Fractals/MandelSet/MandelDef/LogisticMand/LogisticMand.html
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This equation will change how you see the world (Veritasium - Youtube) - https://www.youtube.com/watch?v=ovJcsL7vyrk&t
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What's so special about the Mandelbrot Set? (Numberphile - Youtube) - https://www.youtube.com/watch?v=FFftmWSzgmk&t
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Music used in this video:
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"Arthur Vyncke - A few jumps away" is under a Creative Commons (CC BY-SA 3.0) license.
https://soundcloud.com/arthurvost
Music promoted by BreakingCopyright: https://bit.ly/a-few-jumps-song
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Daystar - Shangri-La: https://youtu.be/-J-ey1JZjUE
Free to use music by https://www.youtube.com/@starryattic
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Lukrembo - Onion: https://www.youtube.com/watch?v=KGQNrzqrGqw
Free to use music by https://freetousemusic.com
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