User blog comment:Hellotheretrespasser/BRP Array Notation/@comment-31966679-20180512190501

So (b(r)p) = lvl(4, lvl(3, b, p), r) = (b ↑ p) ↑↑ r = (b to the power of p) tetrated to the r.

That means your function has a growth rate of 4 for the fast growing hierarchy.