I was going to try mapping out my sleep cycles by waking myself up at random times, one time per night, and then marking it all out on a graph (actually I got this idea last year), and I was wondering, how do the times you sleep affect these sleep cycles?
I mean, can I go to sleep at any time during the evening as long as I always sleep for about ~8 hours and still get the NREM and REM periods at approximately the same time relative to when I went to sleep, or will they change in some way?
That sounds like a neat idea. Different sleep patterns may change up the rythm, however what your giving for an example is more like simply going to bed at a different time. As long as you sleep for your regular 8 hours, the cycles should stay consistent. If you change the actual pattern and start decreasing the amount of sleep you get, you will accumulate sleep debt, which in turn will cause “rebound” sleep stages, where the first stages will decrease in length, and REM cycles will arrive earlier and last for a more pronounced length of time. Not that this is neccesarily healthy for your body, as you still need that deadpan but restorative deep sleep stage (stage 3). But as long as your length of sleep stays consistent, the timing between cycles should stay consisten as well.
… but for mapping your sleep cycles I would suggest to go to sleep every day at the same time and waking up up at the same time, this is the most consistent way that you can imagine and this should help you in mapping out sleep cycles and to be honest if you knew exactly when your REM cycle is then LD’ing would be a ton easier!
Good luck! 
Thank you.
Well actually I am pretty sure one of my REM periods takes place after 5 hours, because I tend to have very vivid dream recall when I wake up at that time.
But it could be fun to map it out regardless.
Well that’s great, you already know a lot. You can start from that. You know that after 5 hours you are in REM, know it would be great to know when it actually starts and you can wake up few minutes before do WBTB and have a full REM cycle ahead! 
I was doing the same few months back and there were good results…
From what I have heard, sleep cycles stay the same no matter what sleep pattern you have, but keep in mind that this is different for every person. I think the only time your sleep cycle changes is when your sleep pattern does permanently.
My comfy sleep time is 10 hours, my first rem period is at about 4-5 hours, and then I believe every 3 hours after. So in a good night I should be able to remember 3 dreams, but some nights I remember more. The way I deduced this, and it’s probably not accurate at all, is because these are the times I would frequently wake remembering a dream. I also found that if I only had 5 hours of sleep, I would wake up remembering one dream. I generally don’t remember any dreams if I only get 3 hours of sleep, at best a fragment.
I know other people have figured out their sleep cycle with the same sort of method, and they have also found that it stays the same unless they change their sleep pattern, in which case they will remember the same amount of dreams in a shorter period.