I have yet to see any signs of this system failing to provide power. I'll keep watching it, but it looks stable.
(...)
I'm starting to suspect that the shape of the channels has something to do with the success or failure of a brownian power-plant. Has anybody tried with exactly the shape seen here? With it rotated ninety degrees? Something about the patterns fluids 'slosh' in might make certain shapes viable while others are not.
Funny, without knowing you had posted this I just built EXACTLY the same structure for the power plant to drive my giant pump stack tower. Er, great minds think alike, I guess? Anyway the thing I did differently was I built the pump in. And I think if you're getting it to work as it is now then you should NOT add the pump; I think having the pump will make it perform WORSE. Mine, which does have the pump, only gets between 200 and 600 total power, and it's very intermittent.
I think this is because the waterwheels only generate power when a unit of water moves past them, but the pump pressure "teleports" the water directly to the end. So instead of passing through every waterwheel in the circuit, the water skips the wheels that have 7/7 water under them and only powers the wheels near the end.
Also, mine is totally closed-loop with the water just recycling from the end back to the beginning; I don't have it connected to a channel or anything. I think that's another problem: the water isn't flowing back into the pump intakes fast enough to keep the pumps full.
Mine is so inefficient I wasn't even able to start it by pumping manually. Ironically designating the channel as a pond and having the dwarves dump buckets of water in there (not all of my channel is 7/7) caused the thing to come to life on its own, just like yours. Honestly I think most of my power is being generated by the dwarves with buckets, not by my pumps! Which gives me an idea on how you could keep up the brownian motion: leave out the pump and just use dwarves with buckets as your only power source! You could use a pressure plate to open a floodgate and let out some of the water when it gets too full.
In electronic circuit design, there are series circuit and parallel circuits. The pump circuits Fossaman and I made are serial circuits. Given the trouble I've had with mine, I'm beginning to think that the right way to do a heavy-duty perpetual motion powerplant is to use a parallel circuit instead. Rather than try to run the water through all the wheels in a snake-like pattern, perhaps it would be better to simply stack six or eight waterwheels shoulder to shoulder in a wide channel. Even if after that you narrow down the channel and only use one pump. In fact, that might even be better than using many pumps. You'd probably want to give the water time to spread out. Oh, and I'm pretty sure the 1-tile-wide "pressurized return pipe" that takes water from the output of the pump back to the beginning should not be a channel, but should run in a tunnel "on top of the floor" until it gets dumped back at the wide part of the channel.
Edit: Just thought of another way to express why I think the parallel waterwheel design will be more reliable: A really succinct way to express it is that I believe when you use the pump it is the waterwheel where the water leaves, or is sucked up into a pump, is the one that is (reliably) generating power. So the goal should not be to get water moving through as many wheels as possible, but to ensure as many wheels as possible get to be ones at the end of the chain.