🚀 go-pugleaf

In article <1992Oct15.144118.27237@viewlogic.com> robl@macro.viewlogic.com (Rob Limbert) writes:
>
>In article <1992Oct14.215137.24498@nntp.uoregon.edu>, scavo@cie.uoregon.edu (Tom Scavo) writes:
>|> ...There is a Julia set
>|> for each  c  and this set lives in the complex plane.  Fix
>|> c  and iterate  z -> z^2 + c  for every  z  you can think of.
>|> For  c  in the Mandelbrot set, the Julia set is connected.
>|> For  c  not in  M , the Julia set is Cantor dust.
>|> 
>
>   In fact, isn't it possible to define the Mandelbrot set as the set of
>all c whose associated Julia set is connected? Something like:
>
>                 M = {c : J is connected}
>                           c

I suppose you could (and many authors do), but it seems more
like a theorem than a definition to me.  It's certainly not the
way  M  came about historically, nor is it calculated this way.

How would you define the bifurcation set (of which the  M  set
is a special case) for some other iteration, like say the cubic
or the complex sine?  Is it known that  J_c  is connected when
c  is in the bifurcation set of the cubic (a 4-d object), for
instance?

-- 
Tom Scavo
scavo@cie.uoregon.edu