"FFFFFFFF" or "DDDDDDD" are random sequences if they're generated by a random process, but we [note: I wonder who 'we' means] expect "random" to mean "frequently changing" or "chaotic-looking".

This might easily be more about formal education in statistics than about culture, though. I'd expect people from any culture we know about to have the intuitive expectations I mentioned -- identifying randomness with chaos.