How Far to the Border?

"How far to the border?"  When dealing with a raster-based set of plates, I need to know where the closest border is for each point on a tectonic plate.  Alas, creating code that answers that question in a timely manner has proven difficult.

Not right

This attempt was reasonably fast, but had only a parting resemblance to the correct result.  The plate boundaries and the centroid of the continental plates should be white, while the rest of the continental plates should be a gradient from black near the boundary to white near the centroid.  Clearly, that's not happening.  So I shall go back to it.

Good night, y'all.