Soul Stories: Tororium

As part of the series of explorations into waves within a boundary, I was trying to find a different way to fold a square into a torus, other than gluing opposite sides.

In my experiments, I was trying to emulate a uniform expanding wave reflecting off a square boundary (no dampening) such that it made interference patterns within. I also tried introducing a circular boundary at the centre of the square (kind of like the Quantum billiards Sinai configuration) to introduce chaos into the system. Now I wanted to see how this configuration would work as a torus.

I made an assumption that beyond the boundary of the square and within the central circle was a singularity (like a black hole). This assumption gave me the freedom to bend the square in an unusual way to form a torus:
Since beyond the square boundaries is a singularity, I pinched all the edges together into a single point; I then attached this point to the central circle/point of the square, but by folding below the surface and attaching. So essentially all the singularity section converged into this single point at the centre of the torus, while the rest of the waves were in the surface. (Hope you get the idea)

This configuration looked pretty interesting to me. It does start with a sort of Big Bang, but then the wave patterns oscillates back and forth (in a periodical motion of ever increasing complexity). Also we can do the same with 1 dimension by pinching the ends of a line segment and its centre and in 3D by pinching the faces of a cube and its centre and so on and so forth for higher dimensions.