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Uh oh! I overthought fizzbuzz.

The following Ruby snippets aren’t quite the same as the automaton above (this Haskell version is actually closest to that), but here’s a couple of Regexp solutions in a style that I haven’t seen before. They have a kind of Turing-tape flavor to them. I’m not much of a golfer, so please let me know in the comments if you tighten them up any.

puts (1..100).map { |n| '1'*n+":#{n}\n" }.join.
  gsub(/^(1{5})*:/,'\0Buzz').gsub(/^(1{3})*:/,'Fizz').gsub(/.*:|(z)\d+/,'\1')

puts (1..100).map { |n| 'x'*n+"#{n}\n" }.join.
  gsub(/^(xxx)*\d/,'Fizz').gsub(/[05]$/,'Buzz').gsub(/^x*|\d*(.+?)\d*/,'\1')