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The standard Collatz function is given by P = 2, a 0 = 1 / 2 , b 0 = 0, a 1 = 3, b 1 = 1. Conway proved that the problem Given g and n, does the sequence of iterates g k (n) reach 1? is undecidable, by representing the halting problem in this way. Closer to the Collatz problem is the following universally quantified problem:
English: This is a graph, generated in bottom-up fashion, of the orbits of all numbers under the Collatz map with an orbit length of 20 or less. Created with Graphviz, with the help of this Python program: # This python script generates a graph that shows 20 levels of the Collatz Conjecture.
Directed graph showing the orbits of the first 1000 numbers in the Collatz conjecture. The integers from 1 to 1000 are colored from red to violet according to their value. French
The Collatz Conjecture. ... But we need proof for all natural numbers. ... If We Draw Graphs Like This, We Can Change Computers Forever. All primes after 2 are odd. Even numbers are always 0, 2 ...
Directed graph showing the orbits of the numbers less than 30 (with the exception of 27 because it would make it too tall) under the Collatz map. For a larger graph containing only odd numbers, see Image:Collatz-graph-300.svg. Created with Graphviz, with the help of this Python program:
English: Directed graph showing the orbits of the odd numbers less than 50 (with the exceptions of 27, 31, 41, and 47, because they would make it too tall) under the Collatz map. For a larger graph, see :Image:Collatz-graph-300.svg. Created with Graphviz, with the help of this Python program:
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Date/Time Thumbnail Dimensions User Comment; current: 20:11, 10 June 2007: 1,315 × 4,195 (99 KB): Keenan Pepper: Directed graph showing the orbits of the odd numbers under the Collatz map.