I disagree. Uniform distribution doesn't violates the assumption of randomness, besides, it is still random, for example, if a certain program will distribute 0-9 integers with the same interval (uniform distribution) the numbers that will be distributed will still random, and it will not stop being random, in my opinion
The numbers on their own (i.e. their particular values) will remain random (i.e. the distribution of their values). But since you distribute them evenly across or along something, that distribution will not
Im not sure if randomness is really absence of pattern. Randomness as in chaotic system can have pattern like fractals, but a small change in starting condition will have unpredictible effect on the outcome. In this view randomness is a product of complexity, as number of input factors and relationship between them. Which is why thermodynamics doesnt work in open systems because entropy dominate.
People seem to be confusing two entirely different things
That is, random patterns with repetitive patterns. The former are the characteristic of a random distribution, while the latter of a distribution which is not random. To make things easier to understand and probably to accept, it can be advised to think about the random patterns as irregularities (or grouping). However, if we consider these irregularities at a higher level, their emergence is not random at all
Which of these definitions says about the lack of random patterns?