Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Fractal behavior of tetration
#1
Let sexp be holomorphic tetration. Let
.
This has fractal structure. This structure is dence everywhere, so, if we put a black pixel in vicinity of each element, the resulting picture will be the "Black Square" by Malevich; it is already painted and there is no need to reproduce it again.
Therefore, consider the approximation. Let
.
While ,
id est, all the points of the approximation are also elements of the fractal (although only Malevich could paint all the points of the fractal).
As an illustration of , centered in point 8+i, I suggest the plot of function in the complex plane,
in the range ,
   
Levels are drawn.
Due to more than lines in the field of view, not all of them are plotted. Instead, the regions where are shaded. In some regions, the value of is huge and cannot be stored in a complex<double> variable; these regions are left blanc.

In such a way, tetration gives also a new kind of fractal.
Reply


Messages In This Thread
Fractal behavior of tetration - by Kouznetsov - 01/28/2009, 03:38 AM
RE: Fractal behavior of tetration - by bo198214 - 02/01/2009, 11:46 AM
RE: Fractal behavior of tetration - by Kouznetsov - 02/01/2009, 06:44 PM
RE: Fractal behavior of tetration - by andydude - 02/28/2009, 10:16 AM
RE: Fractal behavior of tetration - by bo198214 - 02/28/2009, 10:55 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  [2014] The angle fractal. tommy1729 1 2,004 10/19/2014, 03:15 PM
Last Post: tommy1729
  Infinite tetration fractal pictures bo198214 15 21,415 07/02/2010, 07:22 AM
Last Post: bo198214
  Dynamic mathematics , tetration and fractal dimension of a "spiral" Ivars 0 2,811 12/15/2008, 09:18 AM
Last Post: Ivars
  The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] jaydfox 16 16,152 09/09/2007, 01:21 AM
Last Post: jaydfox



Users browsing this thread: 1 Guest(s)