The orbits you see near z=0+1.7i means in those regions the sequence is bounded but doesn't converge to a single number
Show this thread
Convergence of the sequence z, z^z , z^z^z, ... corresponds to spiraling inward to the point of convergence in the complex planepic.twitter.com/1eJOKrmjfn
-
-
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Wait wait wait wait wait so what is tetration(z) as the tetration goes to infinity then?
-
it diverges
- 5 more replies
New conversation -
-
-
it makes for really good tweets
End of conversation
New conversation -
-
-
These spirals resemble a lot the Mandelbrot dynamics. Is there a formal relation??
https://twitter.com/74WTungsteno/status/1222852523205242880?s=20 …
Dynamics in the Mandelbrot Set
https://bit.ly/2Leh05G
#math#science#iteachmath#mtbos#visualization#elearning#geometry pic.twitter.com/LGYFyQUHP0 -
Maybe, converging sequences under iterative conformal maps all must lead to a similar spiral, the rate of spiralling in and the angle between points would be encoded in the magnitude and phase of the derivative at that point.
- 1 more reply
New conversation -
-
-
so it vanishes as n -> infinity ?
-
Diverges
End of conversation
New conversation -
-
-
Okay this one is cool
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.