Watch it join up
The outlined tile in the middle carries 14 ribbon pieces. Step out one block at a time and watch them join into fewer, longer strands, until there is only one.
What you just saw
Each block is one piece of the next, bigger block: 1 tile sits in 9, which sits in 71, then 559, 4,401, 34,649, and on for ever. Inside a small block a strand soon runs into the block’s edge, so the ribbon looks broken into pieces. In the bigger block those edges are inside, the ribbons carry on across them, and pieces join.
The tile’s pieces need three steps out to become one strand. The 9-tile block needs four: try it with the switch above.
Does it really never stop?
Pick a ribbon in any picture and follow it: sooner or later it leaves the picture. Whether it comes back, and where, is decided by tiles outside it, perhaps very far away. Even at 34,649 tiles the one strand still runs out through the rim at both ends; where it goes next is decided in the 272,791-tile block around it, then in the 2,147,679-tile block, and so on.
A picture could show a closed loop, which would settle the question the other way. It can never show that a ribbon goes on for ever and is the only one. That needs an argument about all levels at once.
The spectre, the drawing on each tile, and why only a tiling that never repeats can do this.