Two concepts are helpful at this point. The first, is that all the information needed to specify a sliver may be reduced to a single number. The second, is that between zero and one there is an infinite number of numbers (by using decimals). Therefore, it should be possible to reduce all the information needed to reproduce a particular sliver to a single number.
Take the above tic-tac-toe sliver, for instance. If X is a 2, O is 1, and a space is represented by zero, then, reading from left to right, top to bottom, the information needed to define the sliver would be 102221100. A single number, therefore, is enough to encode the whole diagram.
Now, if we place a decimal point in front of it, we 'squeeze' into something manageable: into a number greater than zero and less than one. And we can manage that for every possible sliver.
That is the first of this post's concepts: the information needed to specify a sliver can be reduced to a single piece of information. The second, is that we may represent that number by a point on a Cartesian plane.
Getting back to our original sliver. We could change one of its pixels. Now, if you change a single pixel of that sliver, you produce a 'neighboring sliver'. Such a pair of slivers would be neighbors on the Cartesian plane. If you change any pixel in the universe, that set of slivers would all fit, as points, about the original point (because there is an infinite number of points around it, more than enough to be able to plot every one-pixel-different slivers).
Getting back to our original sliver. We could change one of its pixels. Now, if you change a single pixel of that sliver, you produce a 'neighboring sliver'. Such a pair of slivers would be neighbors on the Cartesian plane. If you change any pixel in the universe, that set of slivers would all fit, as points, about the original point (because there is an infinite number of points around it, more than enough to be able to plot every one-pixel-different slivers).
In turn, each of those slivers may be surrounded by the one-pixel-different-from-it slivers. So on and so on. Dare I use the term 'ad infinitum'? That's how to envisage the Sliver Catalog on paper.
