Recursive meta cellular systems in 3 dimensions

[lunshen]

Hi everyone,

I recently have become fascinated by an infinitely recursive game of life that uses meta cells to simulate the cells inside themself or the larger ones they happen to make up. A beautiful rendition of this was done (2D) here:
https://oimo.io/works/life/

Would anybody know resources or knowledge about the feasibility of metacells in 3D? Thank you

[dvgrn]

Would anybody know resources or knowledge about the feasibility of metacells in 3D?

They're definitely possible -- in the sense that there are quite a few people around who, if you gave them a few years and a sufficiently generous stipend, would be able to engineer a complete and operational 3D metacell.

However, there are a lot of questions that would have to get answered along the way. The three major ones that occur to me immediately are

1) what 3D CA rule would be used? The sensible thing to do to make this into a workable project would be to design a multistate 3D rule that easily supports signal circuitry. If the rulespace were limited to, say, range-1 3D Moore-neighborhood two-state rules, that might set the project back by months or even years -- because we actually don't know any such rules that support signal processing as well as regular 2D Conway's Life does.

(There are some exceptions, of course. For example, there are 3D rules that can be made to emulate Conway's Life in the center plane of a kind of "sandwich" of 3D cells. But a whole lot of research would be needed to figure out if it's even possible to connect planes of simulated Life circuitry stacked on top of each other, or in different orientations. So the fact that 2D Life can be emulated in 3D doesn't really help us very much: as of now we don't know how to use that fact to build a 3D cell structure that acts like a metacell.)

2) What software would simulate the resulting metacell? 3D CA universes tend to contain a lot of cells, especially on the scale needed to build all the communication and neighbor-counting and decision-making circuitry needed for a working metacell. Recent versions of Golly, for example, can simulate a small volume at reasonable speeds, but this is nowhere near the size you'd need to engineer a 3D metacell.

3) How would the 3D metacell signal its state? Brice Due's metapixel (used in the amazing unlimited-zoom demo that you linked to) turns on a proportion of its cells in an otherwise empty area. Maybe a 3D metacell would include multiple states, and could change the color of its surface to mark its current internal state?

Or would a better plan be a design like the 0E0P metacell, where if a pattern is present in a given 3D volume, that counts as "ON", and its complete absence counts as "OFF"? That would be another big step up in the complexity of the required research, since we would then need a rule that supports 3D universal construction. Again, that's not impossible, but as far as I know there isn't a known universal construction toolkit in a 3D rule that's on the same level of simplicity as Conway's Life.

(Maybe someone has done something universal-construction-ish in Minecraft? I might not know about it if so, but that wouldn't really be an answer to this question.)

[blah]

In general, 3D circuitry is easier than 2D because you don't have to worry about cross-overs, and it's harder to paint yourself into a corner. Admittedly, it's been the better part of a decade since I did 3D circuitry.

They're definitely possible -- in the sense that there are quite a few people around who, if you gave them a few years and a sufficiently generous stipend, would be able to engineer a complete and operational 3D metacell.

Making a metacell takes a few hours or days and no money. I guess you're accounting for creating the circuit simulator/editor, and if it's 2-state, creating the circuit components, but years is still an exaggeration.

2) What software would simulate the resulting metacell? 3D CA universes tend to contain a lot of cells, especially on the scale needed to build all the communication and neighbor-counting and decision-making circuitry needed for a working metacell. Recent versions of Golly, for example, can simulate a small volume at reasonable speeds, but this is nowhere near the size you'd need to engineer a 3D metacell.

A 3D simulator using hashlife exists here. Maybe you don't count it as a CA, though, since large parts can move as singular units, implying information can travel at infinite speed. I also saw a few years ago someone here was working on a hashlife program that supported both 2D and 3D. I haven't been active here for a while; did anything come of that?

Also, classic Minecraft redstone is in principle a cellular automaton. Signals can only be transmitted 15 blocks. I'm sure there are countless redstone simulators you could create a metacell in; my "hours or days" statement would apply there. Also, back in 2009 or 2010 I remember seeing a B3/S23 metacell in Minecraft, so if we're talking about 3D metacells simulating 2D rules, it technically already exists.