Agency in Conway’s Game of Life

by Alex Flint13 min read13th May 202127 comments

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AgencyAI
Curated

Financial status: This is independent research. I welcome financial support to make further posts like this possible.

Epistemic status: I have been thinking about these ideas for years but still have not clarified them to my satisfaction.


Outline

  • This post asks whether it is possible, in Conway’s Game of Life, to arrange for a certain game state to arise after a certain number of steps given control only of a small region of the initial game state.

  • This question is then connected to questions of agency and AI, since one way to answer this question in the positive is by constructing an AI within Conway’s Game of Life.

  • I argue that the permissibility or impermissibility of AI is a deep property of our physics.

  • I propose the AI hypothesis, which is that any pattern that solves the control question does so, essentially, by being an AI.

Introduction

In this post I am going to discuss a celular autonoma known as Conway’s Game of Life:

In Conway’s Game Life, which I will now refer to as just "Life", there is a two-dimensional grid of cells where each cell is either on or off. Over time, the cells switch between on and off according to a simple set of rules:

  • A cell that is "on" and has fewer than two neighbors that are "on" switches to "off" at the next time step

  • A cell that is "on" and has greater than three neighbors that are "on" switches to "off" at the next time step

  • An cell that is "off" and has exactly three neighbors that are "on" switches to "on" at the next time step

  • Otherwise, the cell doesn’t change

It turns out that these simple rules are rich enough to permit patterns that perform arbitrary computation. It is possible to build logic gates and combine them together into a computer that can simulate any Turing machine, all by setting up a particular elaborate pattern of "on" and "off" cells that evolve over time according to the simple rules above. Take a look at this awesome video of a Universal Turing Machine operating within Life.

The control question

Suppose that we are working with an instance of Life with a very large grid, say rows by columns. Now suppose that I give you control of the initial on/off configuration of a region of size by in the top-left corner of this grid, and set you the goal of configuring things in that region so that after, say, time steps the state of the whole grid will resemble, as closely as possible, a giant smiley face.

The cells outside the top-left corner will be initialized at random, and you do not get to see what their initial configuration is when you decide on the initial configuration for the top-left corner.

The control question is: Can this goal be accomplished?

To repeat that: we have a large grid of cells that will evolve over time according to the laws of Life. We are given power to control the initial on/off configuration of the cells in a square region that is a tiny fraction of the whole grid. The initial on/off configuration of the remaining cells will be chosen randomly. Our goal is to pick an initial configuration for the controllable region in such a way that, after a large number of steps, the on/off configuration of the whole grid resembles a smiley face.

The control question is: Can we use this small initial region to set up a pattern that will eventually determine the configuration of the whole system, to any reasonable degree of accuracy?

[Updated 5/13 following feedback in the comments] Now there are actually some ways that we could get trivial negative answers to this question, so we need to refine things a bit to make sure that our phrasing points squarely at the spirit of the control question. Richard Kennaway points out that for any pattern that attempts to solve the control question, we could consider the possibility that the randomly initialized region contains the same pattern rotated 180 degrees in the diagonally opposite corner, and is otherwise empty. Since the initial state is symmetric, all future states will be symmetric, which rules our creating a non-rotationally-symmetric smiley face. More generally, as Charlie Steiner points out, what happens if there are patterns in the randomly initialized region that are trying to control the eventual configuration of the whole universe just as we are? To deal with this, we might amend the control question to require a pattern that "works" for at least 99% of configurations of the randomly initialized area, since most configurations of that area will not be adversarial. See further discussion in the brief appendix below.

Connection to agency

On the surface of it, I think that constructing a pattern within Life that solves the control question looks very difficult. Try playing with a Life simulator set to max speed to get a feel for how remarkably intricate can be the evolution of even simple initial states. And when an evolving pattern comes into contact with even a small amount of random noise — say a single stray cell set to "on" — the evolution of the pattern changes shape quickly and dramatically. So designing a pattern that unfolds to the entire universe and produces a goal state no matter what random noise is encountered seems very challenging. It’s remarkable, then, that the following strategy actually seems like a plausible solution:

One way that we might answer the control question is by building an AI. That is, we might find a by array of on/off values that evolve under the laws of Life in a way that collects information using sensors, forms hypotheses about the world, and takes actions in service of a goal. That goal we would give to our AI would be arranging for the configuration of the grid to resemble a smiley face after game steps.

What does it mean to build an AI in the region whose initial state is under our control? Well it turns out that it’s possible to assemble little patterns in Life that act like logic gates, and out of those patterns one can build whole computers. For example, here is what one construction of an AND gate looks like:

And here is a zoomed-out view of a computer within Life that adds integers together:

It has been proven that computers within Life can compute anything that can be computed under our own laws of physics[1], so perhaps it is possible to construct an AI within Life. Building an AI within Life is much more involved than building a computer, not only because we don’t yet know how to construct AGI software, but also because an AI requires apparatus to perceive and act within the world, as well as the ability to move and grow if we want it to eventually exert influence over the entire grid. Most constructions within Life are extremely sensitive to perturbations. The computer construction shown above, for example, will stop working if almost any "on" cell is flipped to "off" at any time during its evolution. In order to solve the control question, we would need to build a machine that is not only able to perceive and react to the random noise in the non-user-controlled region, but is also robust to glider impacts from that region.

Moreover, building large machines that move around or grow over time is highly non-trivial in Life since movement requires a machine that can reproduce itself in different spatial positions over time. If we want such a machine to also perceive, think, and act then these activities would need to be taking place simultaneously with self-reproducing movement.

So it’s not clear that a positive answer to the control question can be given in terms of an AI construction, but neither is it clear that such an answer cannot be given. The real point of the control question is to highlight the way that AI can be seen as not just a particularly powerful conglomeration of parts but as a demonstration of the permissibility of patterns that start out small but eventually determine the large-scale configuration of the whole universe. The reason to construct such thought experiments in Life rather than in our native physics is that the physics of Life is very simple and we are not as used to seeing resource-collecting, action-taking entities in Life as we are in our native physics, so the fundamental significance of these patterns is not as easy to overlook in Life as it is in our native physics.

Implications

If it is possible to build an AI inside Life, and if the answer to the control question is thus positive, then we have discovered a remarkable fact about the basic dynamics of Life. Specifically, we have learned that there are certain patterns within Life that can determine the fate of the entire grid, even when those patterns start out confined to a small spatial region. In the setup described above, the region that we get to control is much less than a trillionth of the area of the whole grid. There are a lot of ways that the remaining grid could be initialized, but the information in these cells seems destined to have little impact on the eventual configuration of the grid compared to the information within at least some parts of the user-controlled region[2].

We are used to thinking about AIs as entities that might start out physically small and grow over time in the scope of their influence. It seems natural to us that such entities are permitted by the laws of physics, because we see that humans are permitted by the laws of physics, and humans have the same general capacity to grow in influence over time. But it seems to me that the permissibility of such entities is actually a deep property of the governing dynamics of any world that permits their construction. The permissibility (or not) of AI is a deep property of physics.

Most patterns that we might construct inside Life do not have this tendency to expand and determine the fate of the whole grid. A glider gun does not have this property. A solitary logic gate does not have this property. And most patterns that we might construct in the real world do not have this property either. A chair does not have the tendency to reshape the whole of the cosmos in its image. It is just a chair. But it seems there might be patterns that do have the tendency to reshape the whole of the cosmos over time. We can call these patterns "AIs" or "agents" or "optimizers", or describe them as "intelligent" or "goal-directed" but these are all just frames for understanding the nature of these profound patterns that exert influence over the future.

It is very important that we study these patterns, because if such patterns do turn out to be permitted by the laws of physics and we do construct one then it might determine the long-run configuration of the whole of our region of the cosmos. Compared to the importance of understanding these patterns, it is relatively unimportant to understand agency for its own sake or intelligence for its own sake or optimization for its own sake. Instead we should remember that these are frames for understanding these patterns that exert influence over the future.

But even more important than this, we should remember that when we study AI, we are studying a profound and basic property of physics. It is not like constructing a toaster oven. A toaster oven is an unwieldy amalgamation of parts that do things. If we construct a powerful AI then we will be touching a profound and basic property of physics, analogous to the way fission reactors touch a profound and basic property of nuclear physics, namely the permissibility of nuclear chain reactions. A nuclear reactor is itself an unwieldy amalgamation of parts, but in order to understand it and engineer it correctly, the most important thing to understand is not the details of the bits and pieces out of which it is constructed but the basic property of physics that it touches. It is the same situation with AI. We should focus on the nature of these profound patterns themselves, not on the bits and pieces out which AI might be constructed.

The AI hypothesis

The above thought experiment suggests the following hypothesis:

Any pattern of physics that eventually exerts control over a region much larger than its initial configuration does so by means of perception, cognition, and action that are recognizably AI-like.

In order to not include things like an exploding supernova as "controlling a region much larger than its initial configuration" we would want to require that such patterns be capable of arranging matter and energy into an arbitrary but low-complexity shape, such as a giant smiley face in Life.

Influence as a definition of AI

If the AI hypothesis is true then we might choose to define AI as a pattern within physics that starts out small but whose initial configuration significantly influences the eventual shape of a much larger region. This would provide an alternative to intelligence as a definition of AI. The problem with intelligence as a definition of AI is that it is typically measured as a function of discrete observations received by some agent, and the actions produced in response. But an unfolding pattern within Life need not interact with the world through any such well-defined input/output channels, and constructions in our native physics will not in general do so either. It seems that AI requires some form of intelligence in order to produce its outsized impact on the world, but it also seems non-trivial to define the intelligence of general patterns of physics. In contrast, influence as defined by the control question is well-defined for arbitrary patterns of physics, although it might be difficult to efficiently predict whether a certain pattern of physics will eventually have a large impact or not.

Conclusion

This post has described the control question, which asks whether, under a given physics, it is possible to set up small patterns that eventually exert significant influence over the configuration of large regions of space. We examined this question in the context of Conway’s Game of Life in order to highlight the significance of either a positive or negative answer to this question. Finally, we proposed the AI hypothesis, which is that any such spatially influential pattern must operate by means of being, in some sense, an AI.

Appendix: Technicalities with the control question

The following are some refinements to the control question that may be needed.

  • There are some patterns that can never be produced in Conway’s Game of Life, since they have no possible predecessor configuration. To deal with this, we should phrase the control question in terms of producing a configuration that is close to rather than exactly matching a single target configuration.

  • There are possible configurations of the whole grid , but only possible configurations of the user-controlled section of the universe. Each configuration of the user-controlled section of the universe will give rise to exactly one final configuration, meaning that the majority of possible final configurations are unreachable. To deal with this we can again phrase things in terms of closeness to a target configuration, and also make sure that our target configuration has reasonably low Kolmogorov complexity.

  • Say we were to find some pattern A that unfolds to final state X and some other pattern B that unfolds to a different final state Y. What happens, then, if we put A and B together in the same initial state — say, starting in opposite corners of the universe? The result cannot be both X and Y. In this case we might have two AIs with different goals competing for control. Some tiny fraction of random initializations will contain AIs, so it is probably not possible for the amplification question to have an unqualified positive answer. We could refine the question so that our initial pattern has to produce the desired goal state for at least 1% of the possible random initializations of the surrounding universe.

  • A region of by cells may not be large enough. Engineering in Life tends to take up a lot of space. It might be necessary to scale up all my numbers.


  1. Rendell, P., 2011, July. A universal Turing machine in Conway's game of life. In 2011 International Conference on High Performance Computing & Simulation (pp. 764-772). IEEE. ↩︎

  2. There are some configurations of the randomly initialized region that affect the final configuration, such as configurations that contain AIs with different goals. This is addressed in the appendix ↩︎

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31 comments, sorted by Highlighting new comments since Today at 7:24 PM
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Have you seen “Growing Neural Cellular Automata?” It seems like the authors there are trying to do something pretty similar to what you have in mind here.

Yes - I found that work totally wild. Yes they are setting up a cellular automata in such a way that it evolves towards and then fixates at a target state, but iirc what they are optimizing over is the rules of the automata itself, rather than over a construction within the automata.

Wow, that's cool! Any idea how complex (how large the filesize) the learned CA's rules were? I wonder how it compares to the filesize of the target image. Many order of magnitude bigger? Just one? Could it even be... smaller?

Yeah I had the sense that the project could have been intended as a compression mechanism since compressing in terms of CA rules kind of captures the spatial nature of image information quite well.

I wonder if there are some sorts of images that are really hard to compress via this particular method.

I wonder if you can achieve massive reliable compression if you aren't trying to target a specific image but rather something in a general category. For example, maybe this specific lizard image requires a CA rule filesize larger than the image to express, but in the space of all possible lizard images there are some nice looking lizards that are super compressible via this CA method. Perhaps using something like DALL-E we could search this space efficiently and find such an image.

It seems like our physics has a few fundamental characteristics that change the flavor of the question:

  • Reversibility. This implies that the task must be impossible on average---you can only succeed under some assumption about the environment (e.g. sparsity).
  • Conservation of energy/mass/momentum (which seem fundamental to the way we build and defend structures in our world).

I think this is an interesting question, but if poking around it would probably be nicer to work with simple rules that share (at least) these features of physics.

Yeah I agree. There was a bit of discussion re conservation of energy here too. I do like thought experiments in cellular automata because of the spatially localized nature of the transition function, which matches our physics. Do you have any suggestions for automata that also have reversibility and conservation of energy?

I feel like they must exist (and there may not be that many simple nice ones). I expect someone who knows more physics could design them more easily.

My best guess would be to get both properties by defining the system via some kind of discrete hamiltonian. I don't know how that works, i.e. if there is a way of making the hamiltonian discrete (in time and in values of the CA) that still gives you both properties and is generally nice. I would guess there is and that people have written papers about it. But it also seems like that could easily fail in one way or another.

It's surprisingly non-trivial to find that by googling though I didn't try very hard. May look a bit more tonight (or think about it a bit since it seems fun). Finding a suitable replacement for the game of life that has good conservation laws + reversibility (while still having a similar level of richness) would be nice.

I guess the important part of the hamiltonian construction may be just having the next state depend on x(t) and x(t-1) (apparently those are called second-order cellular automata). Once you do that it's relatively easy to make them reversible, you just need the dependence of x(t+1) on x(t-1) to be a permutation. But I don't know whether using finite differences for the hamiltonian will easily give you conservation of momentum + energy in the same way that it would with derivatives.

I recall once seeing someone say with 99.9% probability that the sun would still rise 100 million years from now, citing information about the life-cycle of stars like our sun. Someone else pointed out that this was clearly wrong, that by default that sun would be taken apart for fuel on that time scale, by us or some AI, and that this was a lesson in people's predictions about the future being highly inaccurate. 

But also, "the thing that means there won't be a sun sometime soon" is one of the things I'm pointing to when talking about "general intelligence". This post reminded me of that.

Curated. 

I think this post strikes a really cool balance between discussing some foundational questions about the notion of agency and its importance, as well as posing a concrete puzzle that caused some interesting comments.

For me, Life is a domain that makes it natural to have reductionist intuitions. Compared to say neural networks, I find there are fewer biological metaphors or higher-level abstractions where you might sneak in mysterious answers that purport to solve the deeper questions. I'll consider this post next time I want to introduce someone to some core alignment questions on the back of a napkin, in a shape that makes it more accessible to start toying with the problem without immediatley being led astray. (Though this is made somewhat harder by the technicalities mentioned in the post, and Paul's concerns about whether Life is similar enough to our physics to be super helpful for poking around).

Planned summary for the Alignment Newsletter:

Conway’s Game of Life (GoL) is a simple cellular automaton which is Turing-complete. As a result, it should be possible to build an “artificial intelligence” system in GoL. One way that we could phrase this is: if we imagine a GoL board with 10^30 rows and 10^30 columns, and we are able to set the initial state of the top left 10^20 by 10^20 square, can we set that initial state appropriately such that after a suitable amount of time, we the full board evolves to a desired state (perhaps a giant smiley face), for the vast majority of possible initializations of the remaining area?

This requires us to find some setting of the initial 10^20 by 10^20 square that has [expandable, steerable influence](https://www.lesswrong.com/posts/tmZRyXvH9dgopcnuE/life-and-expanding-steerable-consequences). Intuitively, the best way to do this would be to build “sensors” and “effectors” to have inputs and outputs, and then have some program decide what the effectors should do based on the input from the sensors, and the “goal” of the program would be to steer the world towards the desired state. Thus, this is a framing of the problem of AI (both capabilities and alignment) in GoL, rather than in our native physics.

Planned opinion:

With the tower of abstractions we humans have built, we now naturally think in terms of inputs and outputs for the agents we build. This hypothetical seems good for shaking us out of that mindset, as we don’t really know what the analogous inputs and outputs in GoL would be, and so we are forced to consider those aspects of the design process as well.

Yeah this seems right to me.

Thank you for all the summarization work you do, Rohin.

The truly arbitrary version seems provably impossible. For example, what if you're trying to make a smiley face, but some other part of the world contains an agent just like you except they're trying to make a frowny face - you obviously both can't succeed. Instead you need some special environment with low entropy, just like humans do in real life.

Yeah absolutely - see third bullet in the appendix. One way to resolve this would be to say that to succeed at answering the control question you have to succeed in at least 1% of randomly chosen environments.

I think the GoL is not the best example for this sort of questions. See this post by Scott Aaronson discussing the notion of "physical universality" which seems relevant here.

Also, like other commenters pointed out, I don't think the object you get here is necessarily AI. That's because the "laws of physics" and the distribution of initial conditions are assumed to be simple and known. An AI would be something that can accomplish an objective of this sort while also having to learn the rules of the automaton or detect patterns in the initial conditions. For example, instead of initializing the rest of the field uniformly randomly, you could initialize it using something like the Solomonoff prior.

While I appreciate the analogy between our real universe and simpler physics-like mathematical models like the game of life, assuming intelligence doesn't arise elsewhere in your configuration, this control problem does not seem substantially different or more AI-like from any other engineering problems. After all, there are plenty of other problems that involve leveraging a narrow form of control on a predicable physical system to achieve a more refined control, ex. building a rocket that hits a specific target. The structure that arises from a randomly initialized pattern in Life should be homogeneous in a statistical sense a so highly predictable. I expect almost all of it should stabilize to debris of stable periodic patterns. It's not clear whether it's possible to manipulate or clear the debris in controlled ways, but if it is possible, then a single strategy will work for the entire grid. It may take a great deal of intelligence to come up with such a strategy, but once such a strategy is found it can be hard-coded into the initial Life pattern, without any need for an "inner optimizer". The easiest-to-design solution may involve computer-like patterns, with the pattern keeping track of state involved in debris-clearing and each part tracking its location to determine its role in making the final smiley pattern, but I don't see any need for any AI-like patterns beyond that. On the other hand, if there are inherent limits in the ability to manipulate debris then no amount of reflection by our starting pattern is going to fix that.

That is assuming intelligence doesn't arise in the random starting pattern. If it does, our starting configuration would to overpower every other intelligence that arises and tries to control the space, and this would reasonably require it to be intelligent itself. But if this is the case then the evolution of the random pattern already encodes the concept of intelligence in a much simpler way then this control problem. To predict the structures that would arise from a random initial configuration the idea of intelligence would naturalistic come up. Meanwhile, to solve the control problem in an environment full of intelligence only requires marginally more intelligence at best, and compared to the no-control prediction problem the control problem adds off some complexity for not very much increase in intelligence. Indeed, the solution to the control problem may even be less intelligent than the structures it competes against, and make up for that with hard-coded solutions to NP-hard problems in military strategy.

On a different note, I'm flattered to see a reference in the comments to some of my own thoughts on working through debris in the Game of Life. It was surprising to see interest in that resurge, and especially surprising to see that interest come from people in AI alignment.

Thank you for this thoughtful comment itaibn0.

Matter and energy and also approximately homogeneously distributed in our own physical universe, yet building a small device that expands its influence over time and eventually rearranges the cosmos into a non-trivial pattern would seem to require something like an AI.

It might be that the same feat can be accomplished in Life using a pattern that is quite unintelligent. In that case I am very interested in what it is about our own physical universe that makes it different in this respect from Life.

Now it could actually be that in our own physical universe it is also possible to build not-very-intelligent machines that begin small but eventually rearrange the cosmos. In this case I am personally more interested in the nature of these machines than in "intelligent machines", because the reason I am interested in intelligence in the first place is due to its capacity to influence the future in a directed way, and if there are simpler avenues to influence in the future in a directed way then I'd rather spend my energy investigating those avenues than investigating AI. But I don't think it's possible to influence the future in a directed way in our own physical universe without being intelligent.

to solve the control problem in an environment full of intelligence only requires marginally more intelligence at best

What do you mean by this?

the solution to the control problem may even be less intelligent than the structures it competes against, and make up for that with hard-coded solutions to NP-hard problems in military strategy.

But if one entity reliably outcompetes another entity, then on what basis do you say that this other entity is the more intelligent one?

It feels like this post pulls a sleight of hand. You suggest that it's hard to solve the control problem because of the randomness of the starting conditions. But this is exactly the reason why it's also difficult to construct an AI with a stable implementation. If you can do the latter, then you can probably also create a much simpler system which creates the smiley face.

Similarly, in the real world, there's a lot of randomness which makes it hard to carry out tasks. But there are a huge number of strategies for achieving things in the world which don't require instantiating an intelligent controller. For example, trees and bacteria started out small but have now radically reshaped the earth. Do they count as having "perception, cognition, and action that are recognizably AI-like"?

Well yes, I do think that trees and bacteria exhibit this phenomenon of starting out small and growing in impact. The scope of their impact is limited in our universe by the spatial separation between planets, and by the presence of even more powerful world-reshapers in their vicinity, such as humans. But on this view of "which entities are reshaping the whole cosmos around here?", I don't think there is a fundamental difference in kind between trees, bacteria, humans, and hypothetical future AIs. I do think there is a fundamental difference in kind between those entities and rocks, armchairs, microwave ovens, the Opportunity mars rovers, and current Waymo autonomous cars, since these objects just don't have this property of starting out small and eventually reshaping the matter and energy in large regions.

(Surely it's not that it's difficult to build an AI inside Life because of the randomness of the starting conditions -- it's difficult to build an AI inside Life because writing full-AGI software is a difficult design problem, right?)

I don't think there is a fundamental difference in kind between trees, bacteria, humans, and hypothetical future AIs

There's at least one important difference: some of these are intelligent, and some of these aren't.

It does seem plausible that the category boundary you're describing is an interesting one. But when you indicate in your comment below that you see the "AI hypothesis" and the "life hypothesis" as very similar, then that mainly seems to indicate that you're using a highly nonstandard definition of AI, which I expect will lead to confusion.

But when you indicate in your comment below that you see the "AI hypothesis" and the "life hypothesis" as very similar, then that mainly seems to indicate that you're using a highly nonstandard definition of AI, which I expect will lead to confusion.

Well surely if I built a robot that was able to gather resources and reproduce itself as effectively as either a bacterium or a tree, I would be entirely justified in calling it an "AI". I would certainly have no problem using that terminology for such a construction at any mainstream robotics conference, even if it performed no useful function beyond self-reproduction. Of course we wouldn't call an actual tree or an actual bacterium an "AI" because they are not artificial.

I think the stuff about the supernovas addresses this: a central point is that the “AI” must be capable of generating an arbitrary world state within some bounds.

Well in case it's relevant here, I actually almost wrote "the AI hypothesis" as "the life hypothesis" and phrased it as

Any pattern of physics that eventually exerts control over a region much larger than its initial configuration does so by means of perception, cognition, and action that are recognizably life-like.

Perhaps in this form it's too vague (what does "life-like" mean?) or too circular (we could just define life-like as having an outsized physical impact).

But in whatever way we phrase it, there is very much a substantial hypothesis under the hood here: the claim is that there is a low-level physical characterization of the general phenomenon of open-ended intelligent autonomy. The thing I'm personally most interested in is the idea that the permissibility of AI is a deep property of our physics.

Related to sensitivity of instrumental convergence. i.e. the question of whether we live in a universe of strong or weak instrumental convergence. In a strong instrumental convergence universe, most possible optimizers wind up in a relatively small space of configurations regardless of starting conditions, while in a weak one they may diverge arbitrarily in design space. This can be thought of one way of crisping up concepts around orthogonality. e.g. in some universes orthogonality would be locally true but globally false, or vice versa, or locally and globally true or vice versa.

Romeo if you have time, would you say more about the connection between orthogonality and Life / the control question / the AI hypothesis? It seems related to me but I just can't quite put my finger on exactly what the connection is.

My immediate impulse is to say that it ought to be possible to create the smiley face, and that it wouldn't be that hard for a good Life hacker to devise it.

I'd imagine it to go something like this. Starting from a Turing machine or simpler, you could program it to place arbitrary 'pixels': either by finding a glider-like construct which terminates at specific distances into a still, so the constructor can crawl along an x/y axis, shooting off the terminating-glider to create stable pixels in a pre-programmed pattern. (If that doesn't exist, then one could use two constructors crawling along the x/y axises, shooting off gliders intended to collide, with the delays properly pre-programmed.) The constructor then terminates in a stable still life; this guarantees perpetual stability of the finished smiley face. If one wants to specify a more dynamic environment for realism, then the constructor can also 'wall off' the face using still blocks. Once that's done, nothing from the outside can possibly affect it, and it's internally stable, so the pattern is then eternal.

Random Notes:

Firstly, why is the rest of the starting state random? In a universe where info can't be destroyed, like this one, random=max entropy. AI is only possible in this universe because the starting state is low entropy.

Secondly, reaching an arbitrary state can be impossible for reasons like conservation of mass energy momentum and charge. Any state close to an arbitrary state might be unreachable due to these conservation laws. Ie a state containing lots of negitive electric charges, and no positive charges being unreachable in our universe.

Well, quantum. We can't reach out from our branch to effect other branches.

This control property is not AI. It would be possible to create a low impact AI. Something that is very smart and doesn't want to affect the future much.

In the other direction, bacteria strategies are also a thing. I think it might be possible, both in this universe and in GOL, to create a non intelligent replicator. You could even hard code it to track its position, and turn on or off to make a smiley face. I'm thinking some kind of wall glider that can sweep across the GOL board destroying almost anything in its path. With crude self replicators behind it.

Observation response timescales. Suppose the situation outside the small controlled region was rapidly changing and chaotic. By the time any AI has done its reasoning, the situation has changed utterly. The only thing the AI can usefully do is reason about GOL in general. Ie any ideas it has are things that could have been hard coded into the design.

Seems like there's a difference between viability of AI, and ability of AI to shape a randomized environment. To have AI, you just need stable circuits, but to have an AI that can shape, you need a physics that allows observation and manipulation... It's remarkable that googling "thermodynamics of the game of life" turns up zero results. 

It's remarkable that googling "thermodynamics of the game of life" turns up zero results. 

It's not obvious that thermodynamics generalizes to the game of life, or what the equivalents of energy or order would be: at first glance it has perpetual motion machines ("gliders").

Yup, Life does not have time-reversibility, so it does not preserve the phase space volume under time evolution, so it does not obey the laws of thermodynamics that exist under our physics.

But one could still investigate whether there is some analog of thermodynamics in Life.

There also is a cellular automata called Critters that does have time reversibility.