Indeed, these patterns of outcomes are random themselves (to repeat, I don't question their randomness). But the very fact that there are patterns takes a bit from the randomness of these outcomes making them somewhat less random. In this regard, a uniform distribution seems to be more random on this level, which leads us to question the very idea and understanding of what randomness actually is
There is more pattern in the uniform distribution picture than in the other one. Think about it. If you wanted to guess the next pixel on that picture you would have a much better chance than with the random one
Okay, let's think about it, shall we?
You already see both distributions. But let's assume that you don't. That is, you know nothing about the type of the distribution, whether it is random or otherwise. But you know that any random distribution is, well, random, that any pattern you might look for would also be random. However, you also know that with a random distribution you are bound to find some patterns, and this is not "random" specifically because it is a random distribution
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?