Chickens

Left wing, chicken wing, it don't make no difference to me.

~ Woody Guthrie

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The concept of someone running around "like a chicken with its head cut off" is pretty effective. I can picture that. I can understand the lack of focus and the confusion and chaos. 

However, if you were to say someone was running around "like a chicken"  or "like a chicken with its head still on" I kind of picture the same thing - chicken running around is chaotic with or without its head.