WOLFRAM|DEMONSTRATIONS PROJECT

Collatz Conjecture on a Circle

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color
black
number type
random color
type
CircularEmbedding
SpiralEmbedding
The Collatz conjecture starts with any natural number
n
, then applies
n/2
when
n
is even and
3n+1
when
n
is odd. According to the conjecture, repeating this procedure eventually reaches 1 for any starting number
n
. The sequence of iterates this procedure produces is called the Collatz path of
n
. This Demonstration shows this path for the first
max
integers by arranging the integers around a circle in counterclockwise order from 1 (marked with a circle).