The two phases of 5-tuples generation II
Follow-up to The two phases of 5-tuples generation : r/Collatz.
Still struggling with the 3D space.
The two figures below have the same content:
- The core of the dome for m=1 (orange).
- The sequences of the first number of an example of the two types of bridges* (left and right) with their orange number (n-1 and n+1) for m=1.
- The first column of the other domes (grey) in the third dimension, the rest of each dome being hidden by the first one. The core numbers of dome x being n(x)=m(x)*n(1).
The first figure represents the original dome and allows to connect the orange numbers (n-1, n, n+1) easily. But, as far as I can tell, it is not orthogonal.
The second picture shows an orthogonal space, but the direct link between the orange numbers - and thus between the core and the sides - is lost.
I wonder whether there is a way to take the best of each one in a single display. Or, at least, to clarify the "migration" from one into the other.
* From now on, I will use bridges instead of 5-tuples, as it is more general - 5-tuples and forks being special cases - and allows to treat both sides of a dome at once.
