Beautiful! My jaw literally dropped open .... I have always loved the bifurcation diagram, but never had a clue that it was connected to the Mandelbrot like this. Beautiful. Thank you!
The figure in the wikipedia article (en.wikipedia.org/wiki/Mandelbrot_set#/media/File:Verhulst-Mandelbrot-Bifurcation.jpg Lay, 2008) prompted me to make the video. The Feigenbaum constant would have been found in the Mandelbrot set back in the 1980's, see sites.google.com/site/logicedges/feigenbaum-diagram The Veritasium Logistic map video is very good.
Who the fuck disliked this!? This is awesome but what is even more amazing is seeing the manifold of bifurcation over reals and imaginaries. I'd love to see that given the same treatment.
Yep, saw the Veritasium utb th-cam.com/video/ovJcsL7vyrk/w-d-xo.html - a superb description and explanation of the logistic map, the bifurcation diagram, the Feigenbaum number & link to the Mandelbrot set.
what does the darker or lighter shade of gray in the bifurcation diagram mean? I understand that in the periodic region it's the limit values that the function approaches, but in the nonperiodic region there are these darker lines or darker shading. does it mean that certain values show up more or less frequently in the infinite sequence?
Yes, the darker regions are simply a higher density of points plotted. Each point has been plotted with a transparency to improve the display of point density, which therefore shows the curve regions more clearly. It is worth noting that the curved regions are not directly a predictable result of the sequence of 'x' values (the sequence still follows a deterministic chaotic pattern) but the density of points do follow analytic curves that have been analysed.
The curves in the tree diagram will be related to the parabola used to calculate the logistic map sequence. See The diagrams of iterations here: sites.google.com/site/logicedges/feigenbaum-diagram#h.492d1a88cbc0b781_4
@logicedges I'm a physicist! Just can't imagine someone has mathematical profession and music talent at the same time! Where the science and art meet together at modern time!
I would recommend watching the video "this equation will change your life" (i think that is what its called) by Veritasium, he can explain much better than I can. TLDR: In math even simple equations can have very complex results. One thing an equation can produce is a fractal which is a shape that you can zoom in on forever and still see new features. Two fractals are shown in the video to be related. Both fractals come from very simple equations. It's very fascinating stuff, and their is a lot to learn don't let the math scare you off a lot if it is not that hard 😃👍
Thanks, yes the Veritasium Logistic map video is a very good presentation of the map, fundamentals of a chaotic system and its connections to, for example, a dripping tap. The utb link is: th-cam.com/video/ovJcsL7vyrk/w-d-xo.html
Your website is awesome! I have had it in my bookmarks for years and would read it every now and then. Now some of resources are lost. Were you moving to a new place? If so, love to see it.
Hello, very well done. Would it be possible for me to use this specific render for a video of mine? It is just a poem with assoc. imagery mostly stock footage. I will cite and link back to you in the description of course. (I am too lazy to render it myself and in a rush to put this project together)
Beautiful! My jaw literally dropped open .... I have always loved the bifurcation diagram, but never had a clue that it was connected to the Mandelbrot like this. Beautiful. Thank you!
More incredible : It IS the Mandelbrot! It'a projection of it.
it's the real part of it ... everything else is in the complex plane
Literally had a physical reaction to finally seeing them come together
used java to plot set & bifurcation diagram
11 years and still responding to comments 🫡
I appreciate your video. I finally understood why there are intervened empty lines on the image of the formula.
It is a beautiful relationship between the bifurcation diagram and the infinite number of "mini" Mandelbrot sets.
Best mandelbrot video ever. I wish it was longer. And “not half” version of it would be good too. (transposing images?)
well this just blew my mind
Predates the Veritasium video by 8 years. Very nice
The figure in the wikipedia article (en.wikipedia.org/wiki/Mandelbrot_set#/media/File:Verhulst-Mandelbrot-Bifurcation.jpg Lay, 2008) prompted me to make the video. The Feigenbaum constant would have been found in the Mandelbrot set back in the 1980's, see sites.google.com/site/logicedges/feigenbaum-diagram
The Veritasium Logistic map video is very good.
@@logicedges wow youre still responding, thats dedication
Well thank you, that's great!
This is awesome
Thank you so much for this!
This is beautiful.
Who the fuck disliked this!?
This is awesome but what is even more amazing is seeing the manifold of bifurcation over reals and imaginaries. I'd love to see that given the same treatment.
This was awesome
You should go see Veratasiums video on it, he 3D plots it. Thank you for the heavy lifting.
Yep, saw the Veritasium utb th-cam.com/video/ovJcsL7vyrk/w-d-xo.html - a superb description and explanation of the logistic map, the bifurcation diagram, the Feigenbaum number & link to the Mandelbrot set.
Did I see that right that a minibrot corresponds to a mini copy of the bifurcation diagram?
Yes, the bifurcation diagram comes from the 1D version of the 2D Mandelbrot set map. Both with the matching non-periodic, infinite pattern.
I like the part where the lines split.
how doesn't this have more than 80k views lmao
Do feel free to share! th-cam.com/video/gaOKAtlukNM/w-d-xo.html
(made 9 years ago)
I was prompted to make this video from the excellent "Correspondence between ..." figure at
wikipedia.org/wiki/Mandelbrot_set#Basic_properties
what does the darker or lighter shade of gray in the bifurcation diagram mean? I understand that in the periodic region it's the limit values that the function approaches, but in the nonperiodic region there are these darker lines or darker shading. does it mean that certain values show up more or less frequently in the infinite sequence?
Yes, the darker regions are simply a higher density of points plotted. Each point has been plotted with a transparency to improve the display of point density, which therefore shows the curve regions more clearly.
It is worth noting that the curved regions are not directly a predictable result of the sequence of 'x' values (the sequence still follows a deterministic chaotic pattern) but the density of points do follow analytic curves that have been analysed.
The curves in the tree diagram will be related to the parabola used to calculate the logistic map sequence. See The diagrams of iterations here: sites.google.com/site/logicedges/feigenbaum-diagram#h.492d1a88cbc0b781_4
what is the name of the music ??
🤔Good idea, let's call it "Bifurcating Mandelbrot" 🎹🎶👍
@@logicedgesyou are the creator of this music ?
@@logicedgesBro is still online even after 11 year 😮
Yeh 👍 @@planteruines5619
@logicedges I'm a physicist! Just can't imagine someone has mathematical profession and music talent at the same time! Where the science and art meet together at modern time!
I’m 19, not very strong in Math/Physics and i don’t understand anything... Can someone explain me please ? 🥺🙏🏻
I would recommend watching the video "this equation will change your life" (i think that is what its called) by Veritasium, he can explain much better than I can.
TLDR: In math even simple equations can have very complex results. One thing an equation can produce is a fractal which is a shape that you can zoom in on forever and still see new features. Two fractals are shown in the video to be related. Both fractals come from very simple equations. It's very fascinating stuff, and their is a lot to learn don't let the math scare you off a lot if it is not that hard 😃👍
@@gogglesow1358 Thank you :)
Thanks, yes the Veritasium Logistic map video is a very good presentation of the map, fundamentals of a chaotic system and its connections to, for example, a dripping tap. The utb link is: th-cam.com/video/ovJcsL7vyrk/w-d-xo.html
. I am 9
Your website is awesome! I have had it in my bookmarks for years and would read it every now and then.
Now some of resources are lost. Were you moving to a new place? If so, love to see it.
thanks for the heavy lifting
It was fun seeing the zoomed direct link between the set and the bifurcation diagram after a few hours of the number crunching
Hello, very well done. Would it be possible for me to use this specific render for a video of mine? It is just a poem with assoc. imagery mostly stock footage. I will cite and link back to you in the description of course. (I am too lazy to render it myself and in a rush to put this project together)
Hi, yeh sure - thank you for asking.
WOW
💙🕊
this is the missing constant in the theory of everything
Thank you so much for this!