Hi again.
njsc, your contribution has had so far at least two interesting aspects for me.
First is your remark about group games from the NLP Field Guide. I thought of asking you for their details but finally I decided to leave you the decision whether and when to share with us your knowledge about them and I am going to accept whatever decision you take. An argument for no sharing now is that it might direct our imagination in a specific way and, in fact, limit it. I trust you consider all the pros and cons.
Secondly, you mentioned using mobile phone pictures and Google – and that was entirely unexpected for me. As you will see below my intention was to create a game for, say, seminar participants or crazy party beasts (so the parties could have some extra value 
). Feel free to develop your idea – the more options, the better. Am I right that you intended some kind of on-line game? It can turn out to be interesting for many reasons.
Now, some changes in my thinking occured. I generated an outline of the game and as you can see, I chose a bit different set of ingredients than previously.
In this version there is no leading person inside the game and I banished the showing/naming thing, too.
People playing still stand in a circle facing the centre of it. They simultaneously choose one of the three movements from either alphabet or colours, say, without legs at the beginning. Colours movements probably help better in keeping rythm and a steady pace together at least at the beginning (if there is not any person responsible for rythm outside the circle of players). Everyone says the name of his/her left or right neighbour while making the move.
The next step is to say the name of the next person and move accordingly to the movement done by the previous person. It can be a simple repetition – we do left if it was left, right if right and together if it was together. So, as an example, when I move at the first step I look at Jane on my right side, I observe her movement and say her name. At the next step I look at the next person in the circle, John, repeat previously observed Jane’s movement, observe his movement and say his name. And so I go the full circle over and over (there are a few versions what I do when it comes to me again – in one of them I just continue).
But the repetition is not the only choice. Out of 26 possible sets of substitution rules (pure repetition is the 27th) there are 5 balanced ones:
L—>L, R—>T, T—>R
L—>R, R—>L, T—>T
L—>R, R—>T, T—>L
L—>T, R—>L, T—>R
L—>T, R—>R, T—>L
Maybe clearer presentation of those rules should look like this (upper line of each rule represents all possible inputs, lower shows respective outputs):
L R T L R T L R T L R T L R T
L T R R L T R T L T L R T R L
So probably the easiest transformation is the second one: one just does a mirror reflection of what one sees: left goes for right, right for left and together stays together. But I am sure if the game was used as a warming up for the seminar the other transformations would have been found easy, too.
But this is not the final development of the game. So far our next movement depended solely on the movement of the person whose name we say in the present step. So far so good. Our next movement could depend also on our present movement. This time even the repetition looks far less trivial. For the repetition now means either repeating someone else’s or someone’s own movement or both if they are the same:
LL—>L, LR—>L, LT—>L, RL—>R, RR—>R, RT—>R, TL—>T, TR—>T, TT—>T
or
LL LR LT RL RR RT TL TR TT
L L L R R R T T T
In the set of rules given above (the same set presented in two ways) our previous own movement does not influence the present one (I assume the second letter of each pair to be representing our own previous movement). So even with taking our own movements into account we can arrive at simple repetition of somebody else’s movements. But this does not have to be the case. Have look at this single set of rules:
LL—>L, LR—>L, LT—>L, RL—>R, RR—>T, RT—>R, TL—>T, TR—>T, TT—>R
or
LL LR LT RL RR RT TL TR TT
L L L R T R T T R
In the case shown above we raise left hand as in simple repetition of somebody else’s movement without exceptions. Exception for right hand is when both us and the „imitated” person raised right hands previous time – then we go for „together” (both hands up); and again, an exception for both hands is made when us and the imitated person have made the same „together” movement – then we go for the right hand only.
Out of 59049 possible sets of rules of the kind given above only 1680 (if I am not mistaken) are balanced, ie the number of the possible results L, R and T in the particular set is equal. Fewer rules still, instead of conserving the number of lefts, rights and togethers, promote the aproximate equality of responses throughout the game regardles of the initial input, which is random (it depends on individual decisions of players at the beginning of the game).
Some of the sets of rules should possess the property of causing an arrival at a clearly repetitive pattern of movements produced by the group and individual players. It could serve as an indication for the end of the game: once the repetitive pattern is achieved it proves that everyone stopped doing mistakes – this being probably not achievable without common HPS.
Some versions should exhibit higly complex and hardly predictable behaviour. The repetition period is inevitable with limited number of players and no mistakes, but can turn out to be astronomically long.
Dymitr
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