Noodling around with a protractor, bisecting circles into smaller circles to make them into toroids. Along the way, the 2D drawing displays beautiful symmetries of various kinds.

I imported the drawing into Paint and airbrushed out the compass scratches. I can see toroids all over this drawing, but you may only be seeing the circles. 
This torus and its poles was used to illustrate "the great square within the torus." Same view as the blue lined cutaway above. 
Notice the interesting way this fractal division works. It will go on forever, larger and larger or smaller and smaller, in true fractal manner.
Usually when I've thought about multiplylinked tori, they appear to nest at a single center pole, like Russian dolls. But these new drawings show how the tori can divide fractally along different lines.
Concentric tori courtesy of http://www.multidimensionalmusic.com/review2.html 
The Simple Explanation has also used nesting toroids to illustrate chakras. 
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A little more fooling around in Paint gives us a "quasi torus" in the vertical direction (yellow). Look for more on this tiein to quasiparticles in a future article.