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.