Yes. In fact, in some ways, it's easier to just use a function that gives the odd numbers in the Collatz sequence. See my question for more.

$$(1) \quad o_{n+1}={{3 \cdot o_n+1} \over {2^{v_2(3 \cdot o_n+1)}}}$$

Where $v_2(3 \cdot o_n+1)$ is the 2-adic valuation. $o_n$ is the nth odd number in the Collatz sequence.

You also have the Collatz Fractal iteration, given by,

$$(2) \quad z_{n+1}={1 \over 4} \cdot (2+7 \cdot z_n-(2+5 \cdot z_n) \cdot \cos(\pi \cdot z_n))$$

which extends the collatz function to the complex plane. I think the point to remember is that the way the Collatz function is written definitely influences how it's studied. This allows for new insights about what common threads run parallel to all the methods. We think that thread is convergence to one, but who really knows *yet*?