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.
We as humans have evolved on pattern recognition, it's our basic survival tool, but we sometimes see them where they don't exist. Our pattern recognition has limitations and your pictures exploit that. Trust math, not your eyes. I don't want to start posting pictures of optical illusions - I think you know what i'm talking about.