User blog comment:SuperJedi224/Part 1/@comment-5029411-20140104223015

I have idea:

F_{0,1}(x) = F_x(F_{0,1}(x-1))

F_{n,y}(x) = F_{0,y}(F_{n-1,y}(x-1)) + n

F_{0,y}(x) = F_{0,y-1}(F_{0,y}(x-1))