I am working on creating a material, and have come to a small problem. At some point in my shader I achive this result:

Black-White representation of affected areas

This is basically binary information, either black or white. For my case I am now trying to blur the transition between the black and white areas to achive a softer looking effect in the final result's displacement map. I want to be able to control how large the blur is (thinking of it as the thickness of an outline around the white spots).

I have already researched a fair bit on my own the past few days, but none of the examples I found seemed to apply to my case.