Nils B. Lahr and Clifford A. Reiter, Visualizing Newton's Method on Fractional Exponents, The Visual Computer, 11 2 (1994) 82-86.

Newton's method for finding complex solutions of the equation zα-1=0 is investigated for real values of α. The bifurcations that occur as α varies are illuminated with computer graphics. In particular, the appearance of an attracting 2-cycle just below even powers is investigated.

See also: · Some images[Images]. · Newton's method on systems is discussed in [Abstract mv_1990].