3. Julia Sets and the Mandelbrot Set
3. H. Universality of the Mandelbrot set
|Curry, Garnett, and Sullivan studied
ways in which Newton's method fails to converge to a root, and found
a surprise. Let us see what they found.|
|Newton's method can fail if the starting point lies exactly on the
boundary of the basin of attraction of a root.|
|Can Newton's method have an attracting cycle?
If it does, how would we test this?|
|Here is the experiment of Curry, Garnett, and Sullivan.|
|We learn the Mandelbrot set is almost everywhere.|
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