Why is the Collatz procedure mod 48 ?

I would like to detail the reasoning behind this claim, already made here. We now that numbers can be analyzed in two different ways:

• Mod 16 is the basis for tuples: pairs, even and odd triplets, 5-tuples.
• Mod 12 is the basis for the four types of segments: yellow (even-even-odd), green (even-odd), blue (even-even) and infinite rosa (...-even-even-even-odd).

48 is the smallest common multiplicator of 12 and 16. The figure below details how they interact: