User blog comment:Deedlit11/Extending the fast-growing hierarchy to nonrecursive ordinals/@comment-25418284-20130325203802/@comment-25418284-20130326062509

No ordinals allowed :P

I'm thinking of a function similar to how the xi function "accidentally" produces a growth rate of \(\Phi(1, 0)\). But you can ignore me if you wish; this is just juvenile curiosity with arbitrary rules.