It was me that said they were, not realizing that lack of pattern was one of the definitions of the word "random." That sentence in my post was meant as an acknowledgement of the "lack of pattern" part of the word's definition. Until this thread, I've been using "random" only to refer to lack of predetermined purpose or plan. Now I understand that lack of pattern is also included in the definition.
Not so much "lack of pattern" as occurence of all patterns with the proper frequency.