The Mandelbrot set together with its bifurcation diagram - zoom to magnification × 1,000,000,000

The beautiful Mandelbrot set shown next to its corresponding bifurcation diagram, illustrating how chaotic systems develop. The bifurcation tree relates to the map of the "logistic map zoom" video & can also be used to calculate the Feigenbaum constant, δ = 4.669 201… .

[plovet]

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!

[Snowflake_tv]

I appreciate your video. I finally understood why there are intervened empty lines on the image of the formula.

[annabellesitarek]

Literally had a physical reaction to finally seeing them come together

[sliffy]

11 years and still responding to comments 🫡

[zzuse]

Predates the Veritasium video by 8 years. Very nice

[logicedges]

used java to plot set & bifurcation diagram

[drGokhan_Oz]

Best mandelbrot video ever. I wish it was longer. And “not half” version of it would be good too. (transposing images?)

[alexisandersen]

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.

[Laroac]

You should go see Veratasiums video on it, he 3D plots it. Thank you for the heavy lifting.

[sanchezking]

Did I see that right that a minibrot corresponds to a mini copy of the bifurcation diagram?

[BonesYouTube]

how doesn't this have more than 80k views lmao

[_miobrot_]

I like the part where the lines split.

[CavalloDiSpade]

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?

[Profil_Deleted]

I’m 19, not very strong in Math/Physics and i don’t understand anything... Can someone explain me please ? 🥺🙏🏻

[lazyglimpse]

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.

[a-guess-at-the-riddle]

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)

[II_superluminal_II]

this is the missing constant in the theory of everything