Pattern in mirror-inverted 3D numbers

[Rhuben]

Rules: Compress to single digits to reveal ratio pattern.
The line is to be followed - 1,2,4,8,7,5 and back to 1. Each number being added to itself.The other line is the invisible nines.

Control Dial:

2-D Skin (ignore the +&-)

3-D Torus

Have fun!

 

[dodo]

Let's see. In the first image, the solid lines join powers of 2 (since the number is duplicated on each step). So the image illustrates that a power of 2 cannot be congruent to a multiple of 3 (mod 9), which is something that can be proved by observing that, if 2^n is congruent to r (mod 9), then 9 divides 2^n - r; and since 3 divides 9, then 3 must divide 2^x - r. If 3 divided r it would have to divide 2^x as well, which is false, so 3 cannot divide r.

In the second image you used a different concept; this time not duplicating each number, but adding always the initial number; thus each row represents the multiples of the initial number (mod 9), if you care to replace 9 by 0.

As for the pattern in the third image, or how it ended on the surface of a torus, I'm lost.

 

[Rhuben]