Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
exponential baby Mandelbrots?
The Shell Thron region corresponds to the main cardioid of the Mandelbrot set. Robert Devaney, among others, has studied the exponential Mandelbrot set. For example, see this paper:
The equation Robert Devaney iterates is , where lambda corresponds to the log of the base used for tetration. The parabolic cusp for the exponential Mandelbrot is , which corresponds to tetration for base , which corresponds to the main parabolic cusp of the Mandelbrot set for . The exponential Mandelbrot also has different n-cyclic domains outside the main cardioid, which continue branching in a similar manner to the Mandelbrot set. I wonder whether or not there are baby exponential Mandelbrot copies?

Other resources are the Mandel program by Wolf Jung, which supports exponential iterations under its transcendental mappings. The program also has excellent educational tutorials under its help menu, including discussions of quasi conformal mappings!
- Sheldon

Possibly Related Threads…
Thread Author Replies Views Last Post
  Math overflow question on fractional exponential iterations sheldonison 4 10,110 04/01/2018, 03:09 AM
Last Post: JmsNxn
  An exponential "times" table MikeSmith 0 3,324 01/31/2014, 08:05 PM
Last Post: MikeSmith
  exponential distributivity bo198214 4 10,770 09/22/2011, 03:27 PM
Last Post: JmsNxn
  Base 'Enigma' iterative exponential, tetrational and pentational Cherrina_Pixie 4 14,663 07/02/2011, 07:13 AM
Last Post: bo198214
  Two exponential integrals Augustrush 2 7,619 11/10/2010, 06:44 PM
Last Post: Augustrush
  HELP NEEDED: Exponential Factorial and Tetrations rsgerard 5 13,365 11/13/2009, 02:27 AM
Last Post: rsgerard
  Exponential factorial mike3 3 9,475 10/07/2009, 02:04 AM
Last Post: andydude
  Additional super exponential condition bo198214 4 9,335 10/21/2008, 03:40 PM
Last Post: martin
  exponential polynomial interpolation Gottfried 3 10,887 07/16/2008, 10:32 PM
Last Post: andydude
  U-tetration or "decremented exponential iteration" Gottfried 5 12,011 01/09/2008, 02:14 AM
Last Post: andydude

Users browsing this thread: 1 Guest(s)