Visualizing generalized 3x+1 function dynamics

The function that results in 3x+1 for odd integers x and half of x for even x has led to intriguing questions. The 3x+1 conjecture states that iteration of that function on positive integers eventually results in the value 1. We investigate many generalizations of that function to the complex domain and visualize the resulting dynamics using escape time, stopping time, and basin of attraction images. We will see beautiful, rich dynamics consistent with the conjecture. We see that some generalizations have relatively simple real dynamics, which may make them useful for analysis and we see a complex generalization where sequences of stable egg shaped regions appear in coefficient stopping time images that suggest remarkable patterns for such stopping time.

Title	Visualizing generalized 3x+1 function dynamics
Creator	Dumont, J. P.
Creator	Reiter, Clifford A.
Publisher	Computers and Graphics
Academic Department	Mathematics
Division	Natural Sciences
Organization	Lafayette College
Date Issued	October 2001
Date Available	2015-04-17T19:46:10Z
Type	Article
Language	English
Keyword	Syracuse problem
	Hailstone numbers
	Collatz problem
Bibliographic Citation	Dumont, J. P. and C. A. Reiter (2001 Oct.) "Visualizing generalized 3x+1 function dynamics." Computers and Graphics 25 (5): 883-898.
Standard Identifier	DOI 10.1016/S0097-8493(01)00129-7
Standard Identifier	Handle 10385/1805
Permalink	http://hdl.handle.net/10385/1805
Rights Statement	In Copyright
Rights Holders	Elsevier Science Ltd.