The Universe in Your Eyeball
How can you catch a glimpse of an infinite extent in one single glance? For large objects, you can step back and zoom out, but for…. infinitely large objects?
There is a surprisingly simple technique to represent infinite planes in a finite area.
Let’s first be clear and acknowledge that by representing an infinite object onto a limited area with a discrete resolution (i.e. your screen), we will have to cope with some compromise.
In the case we will see here, that compromise means parts of the represented infinite will feature less detail (or, if you prefer, a coarser resolution).
The idea has been experimented with by several mathematicians and artists in the last century or so; to visualize it, I sketched a quick illustration with Inkscape:
In this sketch we use a simplified model, in that the objects we repeat (a tessellation borrowed from Escher) are placed on a two-dimensional hyperbole, like if we had unrolled an infinite ribbon. The Universe, as we know it, has instead at least three “geometrical” dimensions, but…