Relationship between Mandelbrot set & Logistic map

[@beanz_8193]

As a 9th grader who is interested in both fractals and the logistic map, I’d say your interpretation of both was honestly beautiful and your explanations for both the map and the Mandelbrot set are amazing, thank you

[@manuelgamez8074]

Every appearence of the mandelbrot in any math field it's worth my attention. I recently discovered your channel and let me tell you I love it. Keep it up with great videos!

[@DcubedJ]

Hey thanks for your kind words.. I agree with you in that the mandelbrot set is fascinating and it is cool to see the different properties that emerge from it.

[@desden0va]

awesome video! I just made a video on the same topic, though I talked about a different relationship between the two. I thought about mentioning the fact that they're linear transformations of each other, but I'm glad I didn't since your video covers it so well. I must say, you definitely covered a lot of the introductory topics much more concisely than I 😅 great job

[@DcubedJ]

Hey! Thanks so much for your comment. Ive been fascinated by this relationship so am keen to watch your take on it :)

[@harriehausenman8623]

@@DcubedJ Desdenova linked you video and that's how I got aware of it! Thanks for this content! 🤗

[@harriehausenman8623]

Nice 'collab' 😄

[@matematicke_morce]

My favorite part were the animations starting at around 5:15 onward, I don't think I've ever seen the cycles in the Mandelbrot set visualized this nicely. Also, the music fits extremely well!

[@DcubedJ]

Hey! Thanks so much for your comment. I am glad you enjoyed the visualisations. Please check out the 3b1b and numberphile videos in the references where these types of visuals of the mandelbrot cycles were used. These videos are where I first saw this type of visualisation.

[@harriehausenman8623]

@@DcubedJ I think *they* should link to *you* 😉

[@GiacomoPerin]

What a journey!!

[@harriehausenman8623]

Yes.

[@LittlePaimon]

谢谢！

[@DcubedJ]

Wow, thank you!!

[@geogeo1261]

Thank you for the nice and simplified presentation. Adrien Douady and John H. Hubbard showed the connection of these two diagrams many years ago.

[@Igneous01]

When I look at the logistic map, I can't help but feel like it may be useful to describe quantum superposition sampling, or provide a way to model virtual particle creation/annihilation in the vacuum energy density.

[@jhonatancardona42]

Beautiful and great video.

[@harriehausenman8623]

Love the Ghibli-style music at the end. btw, Desdenova sent me 😉

[@mikedavid5071]

Awesome. Thank you.

[@AyaméLeBobinnec]

this really cleared up some things I was confused about with the logistic map! but arent the logistic map and the quadratic map describing different things after all? I just cant see how their recurrence formula are the same (-rx^2+rx is not x^2+c). and the fractal of the logistic map (which is equivalent to the mandelbort fractal) have nothing to do with each other! i mean, there isnt even any symetry or anything... anyways, maybe i didnt understand correctly, so sorry if i cause any headaches

[@Suav58]

7:11 Technically Linear map is Ax, where A is a matrix and x is a vector whicle Ax +b, where be is another vector is an Affine Map.

[@harriehausenman8623]

Now do: Relationship between Mandelbrot set & Riemann Zeta! /jk

[@MelindaGreen]

You rendered the anti-buddhabrot

[@suraseksonsiri8333]

😲😲👍👍