This snowflake is a variation of a two layered tatted flower that I found on Pinterest. The pin I had for it doesn't lead anywhere. The link is not working or has been removed.
and here is the diagram:
This is done by working the back and then the front petal, the back and then the front.... You join the front petals to the front petals and the back petals to the back petals. I did 7 petals for my snowflake but you could do any number you wanted. To see how I did the top rings, see http://laurasfrayedknot.blogspot.com/2012/11/new-twist-on-tatting-technique.html
Here you can see the two layers of the snowflake.