[Extra Visual] All orbits of the Mandelbrot Set shown together.

This visual shows a series of balls on the complex plane. The equation z=z²+c is applied to every ball once per iteration. Those balls outside the Mandelbrot will escape, and head towards infinity. Those inside the Mandelbrot Set will remain bounded within the radius two circle.

If you look carefully you can see the period motion associated with the periods 2 and 3 bulbs. For example you will notice that the balls return to the period 3 bulb every third iteration. The colour of the balls is graduated for each ball, so that you can get a rough idea of where it started. This graphic shows the first 400 iterations.

In this series:

Extra Visuals (No commentary):

[asherwilkins]

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

[asherwilkins]

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

[THE_ONLY_GOD]

Great visual way to show that! Thanks!

[mnada]

If this beauty is within 2d, I wonder if there is 3d version and how intriguing it would be. Thank you.

[marcielo]

Hi! Pls do all orbits but 1 and 2... these 2 difficult the visualization of the others

[YourPrerogative]

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?

[kinyitom]

YouTube says theres 4 comments but i only see 3