On: The Tale of the Teleporting Turtle (algorithm)

[argv_empty]

* For every full iteration of the loop, TH (tortoise and hare) follows 3 links, while TT (teleporting turtle) follows 1 link.*

Except the TT loop iterations accomplish half as much in terms of covering ground, so TH and TT don't take the same number of iterations.

[JoachimSchipper → argv_empty]

If both Tortoise and Hare have just entered a cycle of length n, the original algorithm takes n iterations before the Tortoise is caught (2n steps for the Hare, n steps for the Tortoise). Likewise, TT takes n steps (although it may take some additional steps before the turtle is teleported into the loop; once this has happened, it's n steps.)

[argv_empty → JoachimSchipper]

* once this has happened, it's n steps* Unless the turtle teleports some time during those n steps. The only way the turtle won't teleport during that time is if the rabbit has already taken at least n steps to get to the loop, in which case, it only eliminates up to 1/4 of the mammal moves.