Your dreams and imagination evolved as a view into another universe. As with the current beliefs, you cannot decipher technical information – no words in books, no details of how devices work, so even if you can describe things you see from another place, you could not reproduce a working version.
Now how do you convince others that the things your are seeing are really happening without being labeled insane? And how could you use this information to benefit yourself or others? Take a peek into the multiverse to see how other versions of yourself have solved these problems…
If our universe is being simulated on somebody’s desktop computer then yeah maybe, but if you were going to simulate a whole universe wouldn’t you at least have a decent random number generator to prevent easily-detectable patterns?
If we assume a malicious intelligence simulating a universe with goal of not being detected, all bets are off – this technique only works in a few cases, and that’s probably not one of them. Also if it’s true, I think we have bigger problems :D
There are a whole bunch of other assumptions too – like the universe running the simulation has entropy and time that work the same way as ours. It’s no magic simulation-detecting bullet – but it’s the only technique I could think of to make any progress whatsoever on the underlying philosophical question! A mote in the eye of a fictional God, so to speak.
In the hard sense, there are no such thing as random number generators on computers. With sufficient starting entropy and computing power, you can generate a mostly reasonable approximation. However, this must use more computing power than not doing it, which is the “signal” we’re sending out to be detected by a fictional observer in the scenario the OP presented.
Interestingly, this technique is used to exfiltrate data from secure computers – e.g. by making the CPU do slightly more work sometimes and modulating that to send data e.g. by radio emission, hard drive noise, power LED brightness changes, and so on. Here’s a generic one for you, if you’re curious: https://thesai.org/Publications/ViewPaper?Volume=9&Issue=1&Code=IJACSA&SerialNo=25
Also, there are sometimes interesting and strange artifacts even with our everyday “random” number generators. I read a really neat paper about that ten years ago, comparing the artifacts of random number generators across operating systems, which sadly I can’t seem to find for you presently. There’s an OK example for you here though: https://www.random.org/analysis/ under “simple visual analysis”.
That kind of weird pattern is pretty typical of most ‘random number’ functions used in software that aren’t security-facing (and sadly sometimes even ones that are). For cryptographically secure random numbers (more like the image to the left than the image to the right on that site), they are more computationally expensive to produce.