My first post (except for the last line) was taken verbatim from "Metallurgy Fundamentals" by Brandt, Goodheart-Wilcox.
Wikipedia has varying perameters for wrought iron depending upon the keywork. (.20% in one and "almost no carbon" in another) I suspect confusion has crept in because anything made of mild steel today is called "wrought iron," so in a modern sense, "wrought iron" averages .10-.18 carbon. Tests I've read about on historic wrought iron indicate carbon below .03% on average.
According to my ASM guide, it goes: "almost zero carbon"= wrought iron, up to about 2%=steel, 2% to about 4%= cast iron, just as stated in "Metalurgy Fundamentals."
My experience forging wrought iron is that it's very "Thirsty" for carbon. If you weld it to steel , there will be carbon migration, and if you work that piece at high temps (which you have to do welding WI) the migration can be severe. If you are getting that pronounced "rotten wood" pattern etch on your material, and your carbon is as high as .11, I'd guess your material is a more refined/worked grade that has been exposed to a somewhat prolonged carboniferous atmosphere (reducing) while being worked, thus soaking up some spare carbon in the process.
It would be great if you could post the pics!!