the swirley patterns you see above are the result of the grain patterns that result from the sanmei construction/lamination process (various steel alloys of varying carbon levels IE varying hardness are welded/forged in a heterogenous mix to make the sword extremely strong and sharp and extremely durible
the patterns at the very edge of the blade are result of differential heat treatment patterns. thick clay is grafted on to the spine of the blade and while thin clay is grafted on the blade. it is then heated at different temperatures and then cooled. the clay on the blade will cool faster.
below is a diagram of the different resulting grain patterns
below is diagrams of archeaologically dug up swords and their lamination constructions
as you can see from the right side of the diagram above, the Han dynasty steel Dao and Jian have forge welded plates of varying carbon levels.
the credit for this process is for some reason given to Japanese people
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