math04hw6

# math04hw6 - (Mathematica C etc draw the Julia set for f z =...

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Homework 6: Due May 24th, Monday, 2010 1. Show that f c ( z ) = z 2 + c has an attractive 2-cycle if c is inside the circle of radius 1/4 centered at -1. 2. The boundary scanning method is the following. For some large number n , if | f n ( z ) | remains within some range then color the point z black, and if | f n ( z ) | escapes that range then color the point white. Using this method, one can draw the “ﬁlled Julia set”. Using your favorite computing language
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Unformatted text preview: (Mathematica, C, etc), draw the Julia set for f ( z ) = z 2 + c for several values of c . 3. Show that the Julia set (the set of points where { f j } are not normal in the neighborhood) is the closure of the repelling periodic points. 1...
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## This document was uploaded on 07/19/2010.

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