GreyArea:
I've used the WS2812 LEDs quite a few times, but always in "series" (I think that's a misnomer as I believe they are actually connected in parallel on the strtip, but what I mean is I always have the LEDs sequentially, so the first LED that's connected to the data wire is LED0, then 1, then 2 etc).
If they're on a manufactured "strip", they are, most likely, in series. Series means DOUT to DIN from one to the next. The power and ground are in parallel, but it's the data lines that determine the type of connection.
GreyArea:
For a project I'm considering now it might be advantageous to connect two strips to a single data output. If I do this, am I right in thinking that the first LED on BOTH strips would regard itself as "LED 0", meaning they would BOTH (or indeed, all, if I have more than two) respond to RGB data sent to them?
For instance, if I currently send
strip.SetPixelcolor(0,255,0,0)
Then on a single strip, the first LED after the data pin will light up red.
That should work. The inputs require only 1µA, so ALL flavors of Arduino have plenty of "headroom" for driving these little guys. And yes, each parallel connected strip will address their LEDs beginning with LED 0, then LED 1, etc.
GreyArea:
But what if there are TWO LEDs attached directly to the data pin? Do the strips have some polite way of working out who goes first, or do they both agree they are pixel 0 and both light up red?
Since parallel connected strips have no "awareness" of their neighbor, they will behave as they would, if they were the only strip connected.
GreyArea:
If I am to connect them in this way, are there any other issues I should be aware of? I know it will mean it is impossible to distinguish between the multiple "pixel zeroes", but in this instance since I want to drive all the strips with the same pattern all the time, that is not an issue.
The only caveat is signal quality, and if parallel connection of strips will degrade the signal enough to push the waveshape [i.e. rise/fall time] outside the stringent specifications.
Keep the wires as short as possible, and a series resistor on each data line [that goes from the Arduino Out, to the first WS2812A DIN], at the WS2812A DIN side, might help. There's a lot of controversy about adding a series resistor. Some, say it's to limit the current should the dataline "ring" and produce voltages that exceed maximum values, or to reduce the slew rate -- presumably to reduce spike and/or ringing. It's more likely to tune "transmission impedance", and is all about snubbing reflections.
My advice? Adding a bit of resistance can't hurt. Adafruit recommends 300Ω to 500Ω. Though, I've seen forum posts by people reporting that much resistance made the LEDs go dark. I suggest trying it, and if the LED don't fire, try reducing it to 200Ω, then 100Ω, etc. The resistor is especially valid for long wire runs to the LEDs. In fact, if the run is very long, like in the range of meters, then you might need a transmission line driver.