After a long time looking deep into the structure of spacetime and after many times turning things inside-out and outside-in, tonight I came to the following conclusion.
Spirorus (spiral torus or torus spiral) is the structure of space-time: Your particles move forward or my waves spread outward or we just turn around, there's no difference!
A spiral torus and a torus spiral are just 2 sides of the same structure which I call "spirorus" (pl. spirori) as illustrated by the pictures below:
The spinning of the spirorus can be seen clearer in the following animation:
And while searching for illustrating images for this post, I accidentally found an interesting spirorus fractal: