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Googology Wiki
Not to be confused with H function.
H* Function
Growth rate
Based On

The H* function (defined by SuperJedi224 for generating new -illions) is defined as follows:[1]

  • H*(m)=H(m)=103m+3
  • H*(m,0)=m
  • H*(m,n+1)=HH*(m,n)(m)=H(H(H(...H(m)...))), with H*(m,n) Hs.
  • H*(a,...,b,c,1)=H*(a,...,b,c)
  • H*(a,...,b,c,d)=H*(a,...,b,H*(a,...,b,c,d-1)) (Although the original definition does not clarify it, the rule is probably supposed to be applied only when d > 1).

In other words:

  1. If there is precisely one variable, the function value is the variable-th -illon.
  2. if there are precisely two variables:
    1. if the second variable is 0,the function value is the first variable.
    2. else:
      1. Decrease the second variable in 1, and call the new function value Z.
      2. The function value is recursion of the first variable through the H* function Z times.
  3. else:
    1. if the last entry is 1, remove it.
    2. else:
      1. Decrease the last variable by 1, and call the new function value Z.
      2. Replace the last two variables with one Z.


See also