[space_fountain]

It need not do any simulation at all. Representing this as an animation should be very doable. Probably 2^4 animations (1 for each potential state of a cell) then you just need to tile the animations and replace sub pixels as needed. So you start out showing a zoomed in view of the animation. As you zoom out you tile based on the animation shown one layer up. The exact tiling is probably tough, but easier than actually simulating and keeping tons of state

[Cthulhu_]

I've also heard that Game of Life can be implemented as a pixel shader, so your browser gets to use all that dank GPU available.

But a looping animation makes sense too.

[symmetricsaurus]

The OTCA metapixel has 2048x2048 cells and a period of 35328. That's a total of 18.5 GB. And that's not counting the different states depending on neighbors and on-off-transitioning state.

Even with compression that's a lot of data.