The 3x + 1 Fractal

ABSTRACT . The 3x + 1 sequence (also known as the Collatz sequence) is generalized to the complex function F: C --> C defined by F(z) = z/2 if ceiling(|z|) is even; otherwise = 3z + 1. Extensions of the well-known 3x + 1 conjecture are considered. A striking fractal in the complex plane C is constructed from iteration of F and a density plot of the resulting modulus. Also, some variants of F are studied.

Download the paper (File: cfractal.pdf, about 316 Kb). To appear in the journal Computers and Graphics 28(3).

©2002 J. L. Pe. Document created on 24 March 2003.