Sketch of the Collatz tree

The sketch of the tree below is a truthful representation, with simplifications. It is based on segments - partial sequences between two merges. There are three types of short segments, the fourth one being infinite:

• Yellow: two even numbers and an odd number,
• Green: one even number and an odd number,
• Blue: two even numbers,
• Rosa: an infinity of even numbers and an odd number.

Here, segments are usually represented by a cell. At each merge, a sequence ending with an odd number (rosa, yellow or green) on the left and one ending by an even number (blue) merge (by convention)..

Rosa segments create non-merging walls on both size, while infinite series of blue segments form non-merging walls on their right. These non-merging walls are problematic for a procedure that loves merging. Sometimes walls face walls "neutrelizing" each other. But one problem remains: the right side of rosa walls. For that purpose, the procedure has a trick: sequences that merge only on their right, leaving the left side facing the walls.

https://preview.redd.it/lhlpbvmpy6ve1.jpg?width=932&format=pjpg&auto=webp&s=7d1d2b6145c60d4ee2e5af923682a461b1d3110f