Mark A. Motyka and Clifford A. Reiter, Chaos and Newton's Method on Systems, Computers & Graphics, 14 1 (1990),131-134.

The chaotic behavior of multivariable Newton's method is explored empirically on systems with fifth roots of unity as solutions. Initial conditions are varied by selection of complex parameters corresponding to screen position in two ways. Some examples illustrate that basins of attraction may be globally dominant in the multivariable case.

See also: · Some Images and animations related to the paper [Images and animations] · Newton's method on fractional exponents is discussed in [Abstract mv_1994b].