# Collatz Paths

Collatz Paths

The Collatz conjecture states that for every positive integer , repeating the simple algorithm

n

n↦

n 2 | niseven |

3n+1 | nisodd |

always eventually reaches the number 1. The conjecture remains unproven since 1937 when it was first proposed by Lothar Collatz.

This Demonstration shows the eventual merging of paths to 1, for all positive integers up to a given maximum. Because the algorithm has two cases, the graph is always a binary tree.