I'm Monday's lecture I showed you some pictures showing the "basins of attraction" for the three complex solutions to z^3-1=0. The applet used to generate those pictures is here. This is another nice page discussing Newton's method in the complex plane. It has several nice examples on display. It also has a more versatile generation form.
The boundaries between the basins of attract on for z^3-1=0 are fractals. Another interesting fractal that I mentioned yesterday is the Mandelbrot set. Wikipedia has a lot of interesting information about the Mandelbrot set, with some really beautiful pictures, like this one.
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