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.
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')
I’m not much of a golfer, so please let me know in the comments if you tighten them up any.
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Comments
I'm a sucker for nice diagrams - did you do it manually or is it generated with a tool?
Thanks, Vidar! I make most of my illustrations, including this one, with Omnigraffle — in fact, it’s one of the reasons that I switched back to the Mac. Nothing automated, just lots of tweaking — which I enjoyed, because I’m trying to learn the rudiments of graphic design, and I usually learn things better if I do them by hand before trying to automate them.
... it's actually the only diagram editor I actually like using. It seemed like that type of visualization of a state machine would be pretty interesting to automate, though, so I was curious if anyone had done it :)
Brainfuck: http://koizuka.nowa.jp/entry/146a3d3b33
>++++++++++[<++++++++++>-]>>>+++>+++++>+<<<<<<
[
>>>+
>- [<<+>>-]<<<+>[<[-]>>>+<<-]<[>>>+++>>[-]<<<<<- +++++++[>++++++++++<-]>.<+++++++[>+++++<-]>.<++++[>++++<-]>+..[-]<]>>
>>- [<<<+>>>-]<<<<+>[<[-]>>>>+<<<-]<[>>>>+++++>[-]<<<<<- +++++++++++[>++++++<-]>.<+++++++[>+++++++<-]>++.+++++..[-]<]>>
>>>
[-
<<<[<+>>>>+<<<-]<[>+<-]>>>>
[
>++++++++++<
[>-[>+>+<<-]>[<+>-] +>[<[-]>-]< [>>+<<<++++++++++>-]<<-]
>---------- >>>[<<<<+>>>>-] <<<<
>>>>>+> >>[-] <[>+<-] <[>+<-] <<<<< [>>>>>+<<<<<+] <
]
>>>>>
[ <++++++[>>++++++++<<-]>> . [-] >[<+>-] >[<+>-] <<<-]
<<<<<
]+
<<<<<
+++++++++++++.---.[-]
<-]