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Show that -i is in the Mandelbrot Set

  1. May 28, 2009 #1
    1a:
    show w = -i is in the mandelbrot set
    show that -1-i is not in the mandelbrot set
    is w= -0.1226 + 07449i in the mandelbrot set, first show that z2 =0

    don't know how to do any of them

    i tried, -(squareroot-1) ^2 = --1, + squareroot -1
    idk
     
  2. jcsd
  3. May 29, 2009 #2

    Mark44

    Staff: Mentor

    What exactly does it mean for a complex number to be in the Mandelbrot set? You need to have this definition in order to tell whether a give complex number is or isn't in this set.

    I don't understand some of the things you have written:
    "z2 = 0" Do you mean z2 = 0? If you don't know how to use the LaTeX controls, you can write this like so: z^2 = 0.

    "-(squareroot-1) ^2 = --1, + squareroot -1"
    I don't understand this at all, but you can write sqrt(-1) to mean the square root of -1 (which is i).
     
  4. May 29, 2009 #3
    For a number to be in the mandelbrot set, it means that it stays within the boundary of that circle thing, and it repeats in a sequence, where a number not in the mandelbrot set dosen't stay in the boundary and dosen't repeat it's sequence

    from that formula, Z1 = Z0^2 + Z0 (each time 0 is incremented by 1
     
  5. May 29, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    This is very poorly written. If you want to be a good itexematician you must learn to be precise and clear!

    You used the word "it" four times without saying what "it" refers to! (And with two different meanings!) You don't say what "that circle thing" is. You don't say what sequence you are talking about and you don't say what "stay in the boundary" means. What you should be saying is that a certain sequence remains bounded. And I can find no requirement that it "doesn't repeat its sequence". If a sequence eventually repeats, it certainly remains bounded.

    from what formula?
    Okay, this is the"formula" you referred to above and that gives the sequence you are referring to. But as given that implies that Z2= Z12+ Z1 which is incorrect. You want Zn+1= Zn2+ c for a fixed number c and Z0= c. When you ask "is -i in the Mandelbrot set" you are taking c= -i. Then [itex]Z_0= -i[/itex], [itex]Z_1= (-i)^2+ (-i)= -1- i[/itex], [itex]Z_2= (-1+1)^2+ (-i)= i[/itex], [itex]Z_3= (i)^2+ (-i)= -1-i[/itex] again!

    It looks to me like that becomes repeating.
     
  6. May 29, 2009 #5
    Sorry, thanks =]
    I know how to use the mandelbrot set now(I think),

    The mandelbrot set was not in my math book, and i didn't take notes during my lecture because i thought it was in the my mathematics book
     
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