Collatz Conjecture on a Circle
The Collatz conjecture starts with any natural number , then applies when is even and when is odd. According to the conjecture, repeating this procedure eventually reaches 1 for any starting number . The sequence of iterates this procedure produces is called the Collatz path of . This Demonstration shows this path for the first integers by arranging the integers around a circle in counterclockwise order from 1 (marked with a circle).
If you choose "number type" for the color control, the lines are colored according to this table: