Search results
Results from the WOW.Com Content Network
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:
Lothar Collatz (German:; July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia. The "3x + 1" problem is also known as the Collatz conjecture, named after him and still unsolved. The Collatz–Wielandt formula for the Perron–Frobenius eigenvalue of a positive square matrix was also named after him.
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.
Collatz conjecture: number theory: Lothar Collatz: 1440 Cramér's conjecture: number theory: Harald Cramér: 32 Conway's thrackle conjecture: graph theory: John Horton Conway: 150 Deligne conjecture: monodromy: Pierre Deligne: 788 Dittert conjecture: combinatorics: Eric Dittert: 11 Eilenberg−Ganea conjecture: algebraic topology: Samuel ...
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
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:
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.
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 .