In a previous post, I shared Christian Freeling’s concept of organicity in games. Freeling describes this concept as follows:
Organicity in abstract strategy games may be defined as “the degree to which a game’s behaviour may be perceived as organic, or ‘life like’”. There’s an objective side to it because Go is felt to be more organic than Chess, almost by consensus. There’s also a subjective side because organic behaviour is a way of perceiving rather than a provable property. And it’s not a quality issue either: Chess and Go are both great games.
If we look at both games in fast-forward, the behaviour of Chess looks mechanical. There are a lot of different kinds of moves and it looks somewhat like a complex sliding puzzle. Go on the other hand has no movement, yet looks like a living, growing organism. An enduring notion that came to my mind after I had just learned enough of the game to suddenly perceive its unity, was that of two conflicting sets of bacteria in a Petri dish. Something alive.
Freeling probes deeper into the concept of organic behavior with an examination of Conway’s Game of Life. He extracts from the Game of Life a list of features which may play a role in the generation of organicity in the system.
A striking example of organic behaviour of ‘pieces’ is John Conway’s Game of Life. The very name illustrates that the game is very suggestive of it and that this is generally recognised as such. If we look at how it actually works we see that …
- it is uniform: there is only one kind of ‘piece’
- it features growth
- it features reduction
- it features movement based on them
- it has a simple protocol to create these features
If these are not actual conditions for organic behaviour, then they obviously have at least some affinity with it. Conway’s game is great to watch and its protocol isn’t hard to understand. In fact it isn’t unlike Go’s protocol: the fate of a piece depends on its neighbours.
Freeling is right to point out the similarities between Go and the Game of Life here. Not only do the fate of pieces depend on their neighbors, but all of Freeling’s five bullet points apply to Go as well as the Game of Life (it’s clear that Freeling’s own game designs are highly influenced by Go as well). This list of features is certainly interesting, but I’d like to dig a little deeper and attempt to get at more fundamental reasons why certain games feel organic. There are a couple such reasons I would like to explore: (1) pink noise in games, and (2) self-self-smilarity across different scales.
Pink Noise
Without getting too much into the technical details, pink noise is a type of randomness in between white noise and brown noise.
In white noise, each state is selected independently of the previous states. In sound, this means that no frequency is emphasized over any other. If you were to play random frequencies at regular intervals, and then you made the intervals smaller and smaller, you would be approximating white noise. Since each state is selected independently of the previous states, there is a high probability that the frequency will often jump abruptly from low to high and high to low. Although we cannot hear the individual ‘jumps’ when we listen to white noise, since they happen too rapidly, pure white noise has a harsh sound (and a high frequency compared to pink and brown noise).
Now suppose that instead of periodically picking a random frequency, you took a frequency and randomly adjusted it up or down very slightly at regular intervals. This way there would be small changes happening in the sound all of the time, but none of the large ‘jumps’ that are characteristic of white noise. This is called brown noise, or random walk noise. It sounds much less harsh than white noise, and is louder in lower frequencies than higher ones.
Pink noise results when the probability of a small change in the frequency is high, but larger changes can happen as well, albeit with low probability. The smaller the change, the more likely it is. This puts it in between white noise, where large changes happen very frequently, and brown noise, where large abrupt changes in state cannot occur.
Brown noise and pink noise are better models of the kinds of randomness we tend to find in nature, since in nature there is often some kind of dependence between a state and the state that follows it.
Pink noise especially is one of the most common signal patterns in biological systems. For instance, this paper argues that when biological systems are given a white noise stimulus, they end up filtering it and delivering a pink noise response. One way of thinking about what might be going on here is a filtering out of irrelevant randomness (i.e., noise), in order to be able to better pick up on the dependencies of one state on the previous state. A low-pass filter can do the same thing in sound design, filtering out the highest frequencies where there is noise in the signal, to allow the sound of the recorded instrument to come through more clearly.
The Wikipedia page on pink noise offers a list of occurrences:
Pink noise has been discovered in the statistical fluctuations of an extraordinarily diverse number of physical and biological systems (Press, 1978;[8] see articles in Handel & Chung, 1993,[9] and references therein). Examples of its occurrence include fluctuations in tide and river heights, quasar light emissions, heart beat, firings of single neurons, resistivity in solid-state electronics and single-molecule conductance signals[10] resulting in flicker noise. Pink noise also describes the statistical structure of many natural images.
Generalizing from literal instances of noise/sound, we can say that a system exhibits pink noise if, at any given moment, there is a high probability of a small change in the state of the system and there is a low probability of a large change in the system.
We can take the generalization a bit further. As Wikipedia notes, many natural images have a pink noise structure. Here, the pink noise has to do not with different states of a system at different times, but rather with the states of the system at different points in space.
Just as people tend to find pink noise the most soothing kind of noise to listen to, we also appreciate systems that exhibit the statistical structure of pink noise.
Part of my hypothesis about what makes a game feel organic, then, is that it exhibits the statistical structure of pink noise in some way, either temporally (at any given time, there is a high probability of a small change in the state of the system and a low probability of a large change in the system) or spatially (for any point in space, there is a high probability of it being quite similar to its neighbors in some respect, and a low probability of it being quite different from its neighbors in that respect). Perhaps brown noise / random walk noise can also feel organic in the right contexts.
As an example of the pink noise in a highly organic game consider the state of a Go board as the game progresses. There is a high probability that that the state of the board will be very similar to its state the move prior; a stone will have been added, perhaps coming with a small capture. But at certain points in certain games a tipping point will be reached and a large group of stones will die with one well-placed move from the opponent.
Now, onto the next feature of organic games.
Self-similarity
One striking feature of Go is that it involves the same sort of fundamental conflict, a fight to surround the other player, at various scales simultaneously. In a local fight, small disconnected groups fight to surround each other, in the hopes of surviving / killing the opponent, while on a larger scale, each player’s stones still aim to encircle the opponent, limiting their growth.
Suppose we dumped equal parts water and oil into the same tank. We might see the same sorts of swirl and droplet formations arising at many different scales. Go is a bit like this. Take for instance, the swirl shape (a pinwheel fight in Go terminology).
First, we have the cross-cut formation, where both White and Black are splitting each other into two weak groups.
Then both players extend from the cross-cut, making what is called a pinwheel formation.
From here, the stones continue to spiral outward, strengthening themselves.
This is a relatively local kind of swirl than can happen in Go, but there are also similar patterns that occur on a broader scale, not with local groups fighting for survival, but with the players’ respective areas of influence. Here too, one player’s influence over one swathe of the board pushes the opponent to seek influence in another part of the board, which in turn pushes the first player again, etc. So we have the same sorts of patterns emerging on a local and global scale.
A brief word about the connection between pink noise and self-similarity. We can see how we might expect at least a shallow form of the self-similarity in a system exhibiting pink noise. If you ‘zoom in’ on a system with many small changes and a few larger ones, we can imagine that we would find even smaller and more frequent fluctuations in between the fluctuations which appeared small when zoomed out but which now appear large.
Back to Freeling’s Criteria
Recall that Freeling gave the following list of factors that might contribute to the organicity of a game in the course of a discussion of Conway’s Game of Life.
- it is uniform: there is only one kind of ‘piece’
- it features growth
- it features reduction
- it features movement based on them
- it has a simple protocol to create these features
Now we are in a position to discuss these criteria in light of pink noise and self-similarity. Can Freeling’s criteria be understood as natural expressions of the two features I’ve discussed?
Let’s take the middle three of Freeling’s criteria as an example. Freeling claims that in organic games, growth and reduction are more fundamental than movement. I’d argue that this is not really a necessary condition on organicity; take a game like Abalone, for instance, which is based on a pushing mechanic, i.e., move your marbles and when appropriate also move your opponent’s marbles. Instead of movement being based on growth and reduction, Abalone features reduction (loss of marbles) based on movement (marbles can be pushed off of the edge of the board). And yet Abalone feels organic, in part because the marbles move one space at a time; a marble never goes from one side of the board to the other. In other words, the changes in the board state are are local and minor. The way in which these small local changes lead to a more significant change in the board state is via marbles being pushed off of the edge, which happens relatively infrequently (most moves do not push off any marbles).
Despite the fact that growth and reduction need not be more fundamental than movement for a game to feel organic, Freeling is still on to something here. When movement is based on growth and reduction, as it is in Go or the Game of Life, this makes it easier to ensure that movement will be gradual and non-uniform. Think of the way an amoeba moves. It does so slowly and non-rigidly, not staying in the same shape but first putting out tendrils and then migrating to those tendrils. Freeling’s idea, I think, is that movement in organic games feels a bit like this. But a protocol based on growth and reduction is not the only way to achieve this kind of effect, it is just an especially reliable way of doing so.
By the way, I think something similar could be said about uniformity of pieces. This is not a necessary condition for organicity, but rather a restriction that makes it easier to come up with rules that generate organic behavior.
There is a lot more to be said about organicity in games, and about our concept of the organic in general, but I’ll leave it there for now.
GAME PRAXIS 