I've always been curious about the process of simplifying 蘭 to 兰. I'm not really familiar with the simplification process, but this one is shocking to me. From what I've seen (I've studied only simplified characters), it's usually easy for me to recognize the similarities between traditional and simplified characters. But here, there appears to be no common basis at all.
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Like a few other simplifications, 兰 is derived from the grass script for the traditional form. The first three strokes are derived from the 草字头 (the grass radical).
Various character forms can be seen on this site.
One thing that's frustrating about this particular simplification is that it's not consistent:
What about all the character which have
Others replace the
This doesn't make any sense to me. I think the nicest thing I can say is that there are some ancient character variants (