Chaotic fragmentation in Halley’s paradise

Computational and graphical results on Halley's method for one-parameter rational functions of the form β1α− 1 = 0 are presented. Level sets for inf (Hβ0n: N = 1, 2, …) and index (β0) reveal a visually striking and intricate class of patterns indicating behavior ranging from stable points to chaos. © 1989 IOP Publishing Ltd.