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An Image from the Collatz Problem open in new window
By Andrew Shapira. The intensity of a point denotes the time taken to terminate.
(http://www.onezero.org/collatz.html)

Collatz 3n+1 Problem Structure open in new window
Observations posted by Ken Conrow to stimulate further research.
(http://www-personal.ksu.edu/~kconrow/)

Collatz Problem open in new window
From Eric Weissten's World of Mathematics. Article with references and links.
(http://mathworld.wolfram.com/CollatzProblem.html)

Experiments with the 3n+1 Sequence open in new window
An online calculator by Alfred Wassermann.
(http://did.mat.uni-bayreuth.de/Fun/3np1_e.html)

On The 3x + 1 Problem open in new window
These pages supply numerical data and propose some conjectures on this innocent looking problem. All numbers up to 29,300 * 10^12 ( ~ 26 * 2^50 ) have been checked for convergence.
(http://personal.computrain.nl/eric/wondrous/)

The 3x + 1 Problem and its Generalizations open in new window
A survey article by Jeff Lagarias.
(http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/p)

The 3x+1 Problem Annotated Bibliography open in new window
By Jeffrey Lagarias, 1997.
(http://www.research.att.com/~jcl/3x+1.html)

The 3x+1 Problem Conference Proceedings open in new window
Katholische Universität Eichstätt, Germany; 5--6 August 1999. On-line proceedings and group photo.
(http://www.math.grin.edu/~chamberl/conf.html)

The 3x+1 Problem Search Results open in new window
Maximum number tested (N): 91·2^50 = 102456891522678784.
(http://www.ieeta.pt/~tos/3x+1.html)

The Collatz Problem, Data and Models open in new window
Properties and predictive models for the Collatz Problem and relative functions.
(http://site.voila.fr/Collatz_Problem)

The Generalised 3x+1 Problem open in new window
A survey by Keith Matthews [PDF].
(http://www.numbertheory.org/pdfs/survey.pdf)

The Structure of the 3x + 1 Function open in new window
Papers by Peter Schorer describing several new approaches.
(http://www.occampress.com/)

The Superset Algorithm open in new window
The "limited halting problem": finding machines that solve the halting problem for limited classes of inputs without reporting erroneous results. The Collatz problem is a special case. Software, papers and graphics.
(http://www8.pair.com/mnajtiv/halt/halt.html)


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