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
.
Return to
the Mandelbrot set and Julia sets
.