Self-existence can be visualised as volcanic islands projecting above the sea. Underneath they all slope into the substrate in which they are one. And the sea is our deluded thought.
The self is a temporary manifestation of the unbroken web of causation. In some senses it exists, and in others it does not. Therefore I speak of the self as existing to convey one point, and as not existing to convey another. It is the meaning that matters, not the words.