User blog comment:Alemagno12/Terminal Array Hydra/@comment-26428969-20151022210141

to reach epsilon-zero quickly, a good way is to "recurse the previous stage" For example:

f(a)[*n] = f(f(a)[n - 1]) f(a)[#[0]#] = f(f(a)[#a#]) f(a)[#[*0]#] = f(f(a)[#[*]a#]) f(a)[#[*n+1]#] = f(f(a)[#[*n]a[*n]a...[*n]a[*n]a#]) Then g(n) = f(n)[[...[[n]n]n...]n] by taking f(n) = n + 1

You don't even need commas! You can use them later to simulate "labels" like for Buchholz Hydras, that's what the R function pretty much do (in a stronger way), see http://googology.wikia.com/wiki/User:Hyp_cos/Linear_Array_Notation