While toying with some of the analogReads, I noticed that my A1 that was connected to my breadboard (a point that had no attachment to any circuit) would return a waveform pattern (see attached image) - I got that by charting the output against the time lapsed ( using millis() ), and estimated the difference between each waveform to be ~3 seconds each. Could someone enlighten me on what exactly I'm measuring with this? Initially I thought it was the AC; but then I thought that runs at 50Hz so this waveform is slower than that.
It might be any device with imperfect shielding somewhere around your setup. A floating pin might take up any ESR from any electrical device that emmits some fields.
I don't think that's it - I'm running it off my laptop, and moved to a room that hasn't got any other electrical devices, and placed the max distance I can from my laptop and the board. I've also tested on 3 other analog pins, which all return identical waveforms. I'm assuming its something to do with the arduino electrical supply, but my electronics knowledge isn't good enough to answer the question
Post a photo of your setup and the sketch you use for testing. It might be the waveform of the USB power but that depends on the code you use.