Is there any 3D patterns, if we are to stack up each generation of "Conway's game of life" on top of each other?

Question

1D Cellular Automata do not show any interesting patterns if we look at each state only one at a time in Succession, but if we put each state below each other, we can see patterns emerging.

In the case of 2D CA like Game of life , we can see patterns emerging if we look at each Generation in Succession. If we apply the same logic used in the case of 1D CA to 2D CA,that is to stack up each generations of 2D CA (for instance,Game of life) on top of each other, Can we expect to see any 3D patterns emerging ?

What do you mean by "interesting"? – Xander Henderson Apr 17 '20 at 03:14 — Xander Henderson, Apr 17 '20 at 03:14
I should have used "patterns" only, I will give it a edit. – Mathews George Apr 17 '20 at 03:17 — Mathews George, Apr 17 '20 at 03:17
Do you mean something like this video? – Ilkka Törmä Apr 18 '20 at 07:00 — Ilkka Törmä, Apr 18 '20 at 07:00
@Ilkka Törmä Yeah, something like that – Mathews George Apr 18 '20 at 10:44 — Mathews George, Apr 18 '20 at 10:44

score 2 · Accepted Answer · answered Apr 18 '20 at 19:50

Yes, if you stack successive GoL configurations on top of each other, of course you can see different patterns. A still life will be a bunch of solid columns of live cells. An oscillator will be a "fuzzy" column that repeats a pattern, and a spaceship is a slanted fuzzy column. Other kinds of configurations produce more intricate 3D shapes.

I'd also argue that we do see interesting patterns in successive configurations of many 1D cellular automata. For example, ECA rule 184 looks like cars in traffic (and can be seen as a very simple model of a highway with traffic jams), which is possibly easier to see from an animation of successive configurations than a 2D picture.

Is there any 3D patterns, if we are to stack up each generation of "Conway's game of life" on top of each other?

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