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The popular method right now seems to be using areas of shapes or heights of bars on graphs when this sort of visual representation is necessary.
However, I like the way you showed it here, mostly because I have wanted to enter repeating sequences of characters like that into a comment on this site to see what it would look like. ;). I hope people represent numbers with long lines of repeating characters on this website more often. I vote for alternating '0' & 'O'.
Though using bar graphs is pretty, it often seems to take up too much space and takes a bit too long to make in some cases. I suppose both bar graphs and unary numeral systems are useful, and which one to use depends on how much space you're willing to use up.
Edit: Also, why alternating 0s and Os? To make counting them easier?