Seeing how at the end of the video all the negative numbers iterate by going back and forth really open my eyes to exactly what's going on when you go in that direction of the mandelbrot set. I just think that's so cool man
No channel has more rewatchability per video than you I swear. Especially the mathemagicigian videos like this one that give you infinite things to learn and observe each time you watch it. It's just so cool to me, I really appreciate you putting these out there
Very helpful! I noticed that there's one period 3 bulb at the far left end of the needle -- it has one ball going back and forth from it, to a point around 1.8, back into the main cardioid (I think), and then back to the original bulb. If you were to zoom in around that seemingly invisible point at 1.8, do you know if you would you see anything particularly interesting?
There is a period 3 orbit within the cardiod of the biggest mini-Mandlebrot on the real number-line. It occurs at about -1.75 from memory. I've animated it in this video: ua-cam.com/video/7MotVcGvFMg/v-deo.html%3A00 (at 23:00 or so).
Actually that orbit that lands in the period 3 mini-Mandelbrot looks like it hits the circle of the mini every 6th iteration, so I think it might even be a period 6 orbit. (The cardioid of that mini-brot is certainly period 3, so the circle would be double that 6). (There are no orbits perfectly on the real number line, just as a result of the way I programmed the animation, otherwise you would see many more on this line.).
Seeing how at the end of the video all the negative numbers iterate by going back and forth really open my eyes to exactly what's going on when you go in that direction of the mandelbrot set. I just think that's so cool man
No channel has more rewatchability per video than you I swear. Especially the mathemagicigian videos like this one that give you infinite things to learn and observe each time you watch it. It's just so cool to me, I really appreciate you putting these out there
Thank-you. I really appreciate the kind words. You'd be amazed at how inspiring nice comments are. :-)
Great visual way to show that! Thanks!
Very helpful! I noticed that there's one period 3 bulb at the far left end of the needle -- it has one ball going back and forth from it, to a point around 1.8, back into the main cardioid (I think), and then back to the original bulb. If you were to zoom in around that seemingly invisible point at 1.8, do you know if you would you see anything particularly interesting?
More like 1.4 sorry
There is a period 3 orbit within the cardiod of the biggest mini-Mandlebrot on the real number-line. It occurs at about -1.75 from memory. I've animated it in this video: ua-cam.com/video/7MotVcGvFMg/v-deo.html%3A00 (at 23:00 or so).
Actually that orbit that lands in the period 3 mini-Mandelbrot looks like it hits the circle of the mini every 6th iteration, so I think it might even be a period 6 orbit. (The cardioid of that mini-brot is certainly period 3, so the circle would be double that 6). (There are no orbits perfectly on the real number line, just as a result of the way I programmed the animation, otherwise you would see many more on this line.).
If this beauty is within 2d, I wonder if there is 3d version and how intriguing it would be. Thank you.
Hi! Pls do all orbits but 1 and 2... these 2 difficult the visualization of the others
Thumbs up
some discussion: www.reddit.com/r/math/comments/g0ccvl/the_mandelbrot_set_visualising_many_different/
UA-cam says theres 4 comments but i only see 3
Yours is the fourth. (Seriously... Replies, deleted spam and 'held for review' also get included in this count I think).
I see tweve including myself even so there's 14