How is this collatz conjecture?

Question

In this video (don't have to see the video as I'm going to give the requierd info) the author defines the $collatz(x,y)$ function as below :

If $x = 3y$ or $y = 3x$ or $x = 2y+1$ or $y = 2x+1$, then the value is $1$
otherwise the value is $0$.

Example :

$collatz(27, 9)$ is $1$ because $27=3\times 9$
$collatz(5, 11)$ is $1$ because $11=2\times 5+1$
$collatz(5, 10)$ is $0$.

How on earth is above definition anyway related to actual collatz conjecture ?

Answer 1

The Collatz conjecture becomes

For any natural number $a$, there is a sequence $a_1, a_2, \ldots, a_n$ of natural numbers such that $$ collatz(a, a_1) = 1\\ collatz(a_1, a_2) = 1,\\ \vdots\\ collatz(a_{n-1}, a_n) = 1\\ collatz(a_n, 1) = 1 $$

And, as he draws the graph later, the conjecture becomes "Any number is connected to $1$ (assuming you draw the graph for large enough inputs)".

Except not really. This function represents a variation on the Collatz conjecture where you divide by $3$ when you can, and if not, you multiply by $2$ and add $1$, rather than divide by $2$ when you can and otherwise multiply by $3$ and add $1$. The tutor probably just got them mixed up.

Also, this function adds paths that would never be valid paths in the Collatz conjecture. For instance, even if you correct it to the right expression, we get that for instance $2$ and $7$ are connected, because $2$ becomes $7$ if we follow the incorrect path of multiplying by $3$ and adding $1$.