The attributes that are speaking of his deity are clearly not communicable. You mention his aseity. I also point to his eternal nature.
However, the attributes that are bound to his personality are communicalbe. For example, grace and love can be found in us.
We have to be careful though to note that while these attributes of God's can be transferred to us, it is actually God in us that brings about these attributes.
See also: Attributes of God
