Here are some real galaxies with the arms identified. Most spiral galaxies have only two arms, though some have as many as six to eight depending on your point of view. If you want to get a good feel for how galaxies look check out the GalaxyZoo's forum they have tousands of spiral galaxies in there. Also as has been mentioned, galaxies aren't generally as tightly wound as yours. Try only one or two windings.
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