I had a really weird thing happen two nights ago. After getting a combined 6 hours of sleep the previous two nights, I was exhausted and ended up going to bed sometime between 12:30 and 12:45. I read my bio textbook for a bit, turned out the light, and lay down, thinking half about dreams and half about everything I had to do the next day. I wasn't aware of any sort of transition, but it seemed I was suddenly aware that I was dreaming, although I was still laying in the same position in bed. A nostril RC confirmed my suspicion. After I got out of bed everything seemed unclear and black, and I almost lost it before I bent over and cemented myself into the dream. It got more vivid as it went on.

When I woke up, the clock showed 1:30am, so the whole thing had to have happened in somewhere around 45 minutes. I didn't think REM came that quickly. What exactly happened here?