I am designing an interactive installation for a gallery where I will receive input telling me which of 8 input transducers have been bridged. For example if someone touches strip number 1, I will be able to detect that. For convenience let’s notate that as {1}. If they touch 1 and 2 simultaniously, I will be able to detect that connection, let’s call that {1-2}. If one person touches strips one and 2, and another touches strips 3 and five, I can detect the state {1-2, 3-5}.
In these lists of connections, any overlap between the sets will just create a union of the sets ie. {1-2, 2-3} would never be detectable, instead I would see {1-2-3}.
My job is to write code that makes events happen in response to these conditions. I will be polling the input and getting a list of groups of touched strips and then …
So my questions are – what are the interesting properties of lists of subsets like this? What kind of patterns can I watch for? What is the formula for enumerating the list of possible groups of connections? The richer my insight into the properties of this data, the better I can map it to interesting and appropriate events. Mapping can be memoryless (ie. deterministic for a given input state) or it could reply to sequences, or even the timing of sequences. I have a few clues of directions I could take this, but I am hoping some folks with a bit more knowledge of algorithms and sequences will be able to give me some pointers here.
You seem to be partitioning a set of transducers. Just consider any unbridged transducer a singleton set.