User blog comment:Billicusp/UBAF/@comment-27173506-20151230193358

Well, your function reaches the growth rate f_w(n), and your gugorimax is about f_w+1(f_w(100)). You see, the last level utterly dominates the previous ones. To see why, let's generalize each stage:

n+n+n...+n n+n times=n*(n+n)=n*n*2

n*n*n...*n n*n times=n^(n*n)=n^n^2. (Way bigger!)

n^n^n...^n n^n times=n^^(n^n)=n^^n^^2 (Even more so!)

n[m]n[m]n...[m]n n[m]n times=n[m+1](n[m]n)=n[m+1]n[m+1]2

Where the square brackets are hyperoperators. The concept of recursing through all of the previous stages is interesting though.