So how random is it really? If you see a dot, aren't you more likely to see another dot nearby with such a distribution? But that means things are no longer random to you even if the distribution of dots itself remains totally random. You take advantage of some feature or property of a random distribution that any random distribution has (namely, patterns), and thereby you stop it being random despite it being random. Isn't it a nice paradox or conundrum?
There is no such thing as "random to you", at least there is no use for such a thing unless you're into some weird art forms. For any practical use of randomness, such as gambling or cryptography or statistics, math trumps human perception of randomness
Well, let's discuss it
You seem to be basing your opinion on an axiom that random has patterns but it doesn't. Despite the appearance of patterns (alltho I can't say that I see any patterns in your second picture - a few dots next to each other is not a pattern) there are no proven patterns in, for example, bitcoin RNG. Which has a big big incentive to be cracked, wouldn't you agree? So random is random
It is not like I just saw that picture and decided to start a discussion here
It means I came prepared for a thorough clash of opinions. Here's my story (for the sake of "practical use of randomness"). I have an acquaintance which I hadn't seen since like 2012 till this summer. We met in last July, and we both made a point that we hadn't seen each other for about 7 years. Then he said that we would likely not see each other again for another 7 years
Obviously, I expected better as I was already well aware that random events of the same type have a tendency to come together, one after another. And what do you think? In a week or so I met him again in a totally different place under totally different circumstances (even at a different time of the day, for that matter). He was surprised but I definitely was not. In fact, I actually felt like we were going to meet again pretty soon (this is the practical part of all it)
But then it was my turn to be surprised as in a couple of days we met once more in a completely different setting (needless to say that my acquaintance was completely flabbergasted). Me, I didn't really expect that such an event was going to repeat itself again, either, as I thought these two encounters in so short a timespan was more than enough. And we haven't seen each other since summer (and probably won't for another 7 years, right)
That said, I don't know how it can possibly trump "human perception of randomness" as this perception, as you call it, allows to override the randomness of something, and make decisions precisely based on that randomness (or rather its override). I don't know either how that can be construed as an impractical use of randomness as it is quite the opposite. To sum it up, if you encounter something ostensibly random and seldom, expect more of it in about or around
So how random is it really? If you see a dot, aren't you more likely to see another dot nearby with such a distribution?
In a truly random distribution you should expect another dot anywhere with an equal chance, including next to the first dot. It is not more or less likely. It's an optical illusion. On the contrary, if no dots at all have another one nearby that is definitely not random
Then what about stars being grouped in galaxies? This grouping is said to be entirely random as otherwise the whole theory of the Big Bang doesn't hold. I think you can't go beyond that as far as randomness is concerned as there is no manifestation of randomness of a larger scale. Is this an optical illusion too according to you?