Here is a graph showing the orbits of all numbers under the Collatz map with an orbit length of 18 or less, excluding the 1-2-4 loop.
The Collatz conjecture is as follows.
The conjecture is that you will always reach 1, no matter what number you start with. At this point, of course, you end up in an endless loop going from 1 to 4, to 2 and back to 1.
Alternatively, we can formulate the conjecture such that 1 leads to all natural numbers, using an inverse relation (see the link for full details).
If we exclude the 1-2-4 loop, the inverse relation should result in a tree, if the conjecture is true.
Collatz graph generation based on Python code by @TerrorBite. Radial node-link tree layout based on an example in Mike Bostock’s amazing D3 library.