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The most interesting things that have been done, that I know of, via the circuit network are :
A video set to Danude's Sandstorm,
A game of Tetris,
A mini first person shooter using vector logic.
You can find discussions for these things, and others, on the official forums.
My own use of the circuit network is pretty basic; I just use it to monitor a supply station (such as an Iron Ore Mine or a Coal Mine) to enable/disable the station depending on whether there is enough material for a full load, to control how much an inserter puts into a chest, and to control oil products to determine when to send heavy and light oils to cracking.
Re: nuclear power, get a small moduled/beaconed Kovarex plant set up and there is no reason, other than the desire to do so, to try to conserve U235. My own efforts in that area, before I gave them up as totally unnecessary, involved monitoring a Storage Tank for steam. I had the fuel inserter set to Stack Size 1, and to only operate if the spent fuel removing inserter had any spent fuel in hand. The spent fuel removing inserter was set to turn on only if there was not enough steam in that Storage Tank. So, reactors generate heat, the power plant turns that heat into steam, and then when the fuel is spent 200 seconds later, the plant is still converting the heat to steam. Eventually enough steam gets used that the level in that tank drops low enough to trigger the removal of the spent fuel cell, which in turn triggers the insertion of a new fuel cell.
If you want a "crash course" in some of the more advanced applications of the circuit network, give the AAI modpack a try. Just make sure to use the AAI features (use the mining vehicles and haulers and such, rather than burner and electric miners) and don't look online for BP's.
https://i.imgur.com/QDgxovO.png
I got the idea to use bit shift to switch display patterns from a forum thread but I figured out all the combinators and calculated all the constants myself.
Also used circuits to make a "perfect" sushi belt for science.
https://i.imgur.com/eGSlefU.png
I mostly use circuits for things that lots of people do, because I like my circuits to be beneficial to my base, not just be there for no reason. If it is beneficial chances are a lot of people are already doing it. Mostly circuits are good for controlling production (eg to turn on and off cracking using pumps), for alarms, kovarex, train stations.
The checker board traps the bugs and holds them in place while the flame throwers and turrets rip them to shreds. It keeps the spitters from getting close enough to spit since the biters have all ready triggered the gates at that point.
Instead it interlaces two same-name unloading stations so that exactly one is active. The "near" one is disabled by placing a signal right in front of the train station, the other is disabled by stopping the actual belts.
That way, only one train is actively unloaded until completely empty, then the other one immediately starts unloading.
This alternating behaviour is controlled using a rather simple combinator setup.
I’ve built it to spare using 12 buffer chests for each wagon, as these are either always full (if more source material is produced than consumed) or always empty (if more is consumed than produced).
It only had one lane turn left but you can draw right turning paths and connect them to chain signal circuits and it would work very well in my case - it made up for cost of rails and chain signals, was small - The thing is that the game has it's own computations for these mechanisms so trains for example find their own routes - but if you create those circuit conditions for right hand turns it would work completely acceptably
I made a power switching system and it works - the capacitors don't drain - but I guess the reason why is because it's not using up all that energy now that it switches off every tick it's only using like 50% or less for the actual power output ---- buuut the actual power output brown outs - this way it's always partially green
But I mothballed it because I got frustrated with the inevitable 'thundering herd' problem where all available trains stampede towards the same recently opened station all at once.
Thinking of pulling it back out now that the upcoming 1.1 update will add the train stop limit feature, and retrofitting it. Or maybe just starting fresh on a completely new system.
I had also wanted to at one point to try my hand at building a basic packet switching solution on top of the circuit network. Could also be very cool for train logistics circuit networks as they're typically long-distance; highly interconnected and thus congested.
However, I realized a packet switching solution would probably be huge and simply outside of the realm of practicality to plop down next to each station or sub-factory that needs to uplink to the long-distance network. So I skipped out on it. (I generally don't build stuff for the "just because" factor; somewhat similar to Hedning, I want some utility out of it.)
The more common solution taken there is to build a timer and take one wire as the clock signal which time-slices 'slots' across the long-distance network, while the other wire serves as the data signal. So I guess I'll stick with that one and maybe build a nice little abstraction around it.
https://steamcommunity.com/sharedfiles/filedetails/?id=1093906243