For me at least, it seems to depend on why I'm sleep deprived and what I'm doing. I spent 100 hours straight through working on my dissertation (only breaks to go fetch food etc.), and felt fine for the entire period - no fatigue, no noticeable cognitive effects, I was alert and coherent - right up until I stopped writing. Then it all just hit me all at once - speaking coherently was a challenge, there was an afterimage if I looked around too quickly, my mind was full of scattered and fragmented half-thoughts (not dreaming, but a similar feeling), and I ended asking a friend to go with me to a building I'd been to hundreds (possibly thousands) of times because I wasn't sure I'd find my way there. To put it simply, I was mentally a mess, and just needed to crash for 18 hours to recover.
On the other hand, I'm currently sleep deprived due to insomnia (it's 1320 on Tuesday, and I've had less than an hour sleep since 0900 on Friday), and the effects have been much more gradual. It's a steady build-up of fatigue and general "brain slowness" for lack of a better word (e.g. I was playing Picross last night, and puzzles that normally would take me less than ten minutes took me more than half an hour), but I'm more or less fine - no visual effects, my thoughts are coherent, and it doesn't feel much different to how I'd be after a long day working (just significantly more severe).
That's amazing to me. I haven't been over 20 hours without sleep for several years, before that I think the max I did was about 35-40 hours which was enough to almost make me hallucinate. I guess I could go for longer, but at that point the only thing I want to do is sleep, any other life goals suddenly become distant second in importance.
It's certainly not something I'd recommend doing (I've had a couple of occasions where I've been up 40ish hours and started to notice the visual disturbances, so it can definitely come on sooner).
The dissertation was partly very poor planning on my part, but I also stumbled on a doctoral thesis that more or less disproved the central tech. behind my dissertation less than a week before the final deadline, which gave me two options:
A) finish up what I'd done, knowing it was fundamentally flawed and that I'd never be able to defend it if called for a viva voce (unlikely, but a definite possibility)
B) rewrite pretty much the entire thing (~30k words) to take a different approach, re-implement the hardware (audio filtering; didn't help that the spec. sheet lied to me and said it had an FPU but actually just emulating floating-point in software which was unusable slow), and come up with a convincing conclusion explaining why a year-long project produced nothing particularly useful.
I went with B, hence the 100 hours of solid work, and it went OK (mark was a marginal pass, but a pass nonetheless), but I'd hate to do it again. It took me 3 or 4 days to start feeling normal and alert again, despite sleeping 18 hours after crashing once it was finished.
The current insomnia is really weird though. I saw my GP this morning, took a fairly hefty dose of sleeping aids (15mg diazepam on top of the 20mg tamazepam and 75mg promethazine I was already prescribed[1]), yet somehow feel more awake than before taking those, despite the fact I'm only about three hours away from having had less than than an hour sleep total in the last six days. Honestly, I just feel bored more than anything at this point (hence this somewhat unnecessarily long post :p) - I don't have the physical energy to do a great deal, but mentally I feel more or less normal (though I suspect when I finally do get some sleep, it'll catch up with me and I'll have a rouge couple of days).
[1] FWIW, I've also got Zopiclone, but I saving that as a dug of last resort. The benzodiazepines cause me no side effects, but last time I used the Zopiclone it was rather unpleasant - it caused mild hallucinations (my room looked like it was bathed in a lemon-yellow light, despite it being the dead of night and no lights were on), and it had a strong amnesiac effect (my memory of the night pretty much goes "I'm in bed, why is everything yellow?", "I'm in the bathroom, how did I get here?", "I'm back in bed, but it's three hours later", and I have literally no idea what happened between each thought. It's just like a jump cut in a movie - there isn't even a hazy memory of I did something; it literally just goes from being in one room to being in other, despite there obviously being a chuck of time missing. It's pretty disconcerting).
On the other hand, I'm currently sleep deprived due to insomnia (it's 1320 on Tuesday, and I've had less than an hour sleep since 0900 on Friday), and the effects have been much more gradual. It's a steady build-up of fatigue and general "brain slowness" for lack of a better word (e.g. I was playing Picross last night, and puzzles that normally would take me less than ten minutes took me more than half an hour), but I'm more or less fine - no visual effects, my thoughts are coherent, and it doesn't feel much different to how I'd be after a long day working (just significantly more severe).