I was watching the excellent video Cold Mac video from @mdoudoroff last night and had the thought… is eurorack - specifically pure CV stuff - Turing Complete? It almost certainly is, right? Let us omit modules like teletype that are already computers. Magic: the Gathering is. And a whole bunch of other things “accidentally” are.
Is there any existing research on this?
I haven’t thought it through, but I wouldn’t be surprised if this doodad would accelerate matters.
Take any CV sequencer that can move in both directions and you have a (finite length) Turing tape. Then just stack infinitely many of them next to one another to have the infinite Turing tape. (Technichally, the tape contents of a Turing machine are always finite, but unboundedly finite, hence the infinitly many sequencers 
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Then you only need finite control with some logic gates. So yeah, it’s Turing complete
You might be able to formulate a Turing machine from W/ (tape) and Cold Mac (processing) alone, though you also need some state “register” storage in addition to “program” tape. So perhaps more than one of each.
I think the short answer is: yes. But the real question is what do you want to compute, and how big is your budget? After you start stacking 100s of logic gates together, you’ll start rediscovering all the usual problems with circuit design, like propagation delays, rise times, clock skew, etc. If you allow yourself to use one of the computers-in-a-module options, then you’ll be able to compute a lot more stuff with fewer problems – and, in my humble opinion, less fun.
I believe comparator(s) are also used to derive square waveforms from an oscillator with a saw or tri core. I think this is also how PWM is done: you are modulating the threshold.
You’re absolutely right. What’s fun depends on the person, the state of mind, the goals, etc.
It would be interesting to have a system with, say, 1000 comparators (complete with LEDs for “easy” debugging) and 1000 attenuators. Such a system would also be useful for educational purposes (“now build a 4 bit adder circuit”) and you could probably make some interesting sounds, too.
Turing compete is an interesting mathematical construct, but for the purposes of a synth doesn’t seem tremendously helpful; additionally, something being Turing complete doesn’t mean it’s practical to use for general computational purposes. Specifically, treating your eurorack as an analogue computer wouldn’t offer much benefit in musical terms, and certainly no benefit over putting a more conventional computer in your rack. In short, it’s an interesting thought but probably not that relevant to your use (for music, or more generally audio) creation on the system.
But digital computers are so cold!
Besides, I use a digital computer all day at work, the last thing I want to do is sit at another one at home 
In terms of computing as medium of interest in its own right, it reminds me of something I’ve not thought of it a long time: the game “core wars” (and to a lesser extent 1k/4k intro programming). I suppose there may be interesting approaches that stem from low level constructed simply as a form of art in their own right. I guess the hard part would be finding the medium by which a consumer could enjoy it.
Thinking out loud, I wonder if any of the earlier analog computation models (I believe economics was modelled this way) make interesting sounds if run on a modular. The building blocks would be all available within normal synthesis modules (I believe), and I seem to remember various economic models produce oscillations…
Reference to this here - https://en.wikipedia.org/wiki/MONIAC
Coloured liquids - i’m now wondering if this could make a cool interactive instrument/installation thingamabob