Question: Is it known that hailstones are (relatively) short ?

Follow to [Facing non-merging walls in Collatz procedure using series of pseudo-tuples : r/Collatz](https://www.reddit.com/r/Collatz/comments/1jmixz4/facing_nonmerging_walls_in_collatz_procedure/)

As I haven't worked on hailstones, I allow myself to ask users to share their experience.

If the answer to the question is positive, I might have an explanation.

The mentioned post shows that the procedure generates converging series of preliminary pairs* that alternate odd and even numbers (green segments), generating quick rises in sequences.

So far, I saw them as part of the isolation mechanism*.

This happens within triangles* that grow slowly. The figure below shows, based on the example in the mentioned post, the log of starting number of a sequence involved in a series (green) and the log of the length of this series.

There are many triangles - starting every 8n - that show the same pattern.

So, even with very large starting numbers, the length of the series remains (relatively) short.

This would mean seeing only short "surges" within any sequence. Maybe somebody noticed that.

Thanks in advance for your comments.

https://preview.redd.it/v1tew7ti202f1.jpg?width=3006&format=pjpg&auto=webp&s=7473cb680dc1306386020963a084eb058316bd87

* [Overview of the project (structured presentation of the posts with comments) : r/Collatz](https://www.reddit.com/r/Collatz/comments/1k98c5a/overview_of_the_project_structured_presentation/)