Fast Growing Hierarchy Calculator -
function eval(ordinal α, int n, limits): if α == 0: return n+1 if α is successor β+1: return iterate(eval(β, ·), n, n, limits) if α is limit: λn = fundamental_sequence(α, n) return eval(λn, n, limits)
To give you a sense: ( f_\omega^\omega(3) ) is a number so large that writing it down in standard notation would require more digits than there are particles in the observable universe—by an absurd margin. fast growing hierarchy calculator
if isinstance(alpha, int): if depth > 3: # Limit output depth return f"prefix -> (Massive Iteration)" function eval(ordinal α, int n, limits): if α
The "Fast Growing Hierarchy" (FGH) is a framework used in googology (the study of large numbers) to compare the growth rates of functions. Because the values produced by this hierarchy quickly become too large for standard computer arithmetic (even exceeding the estimated number of atoms in the universe within the first few steps), a "calculator" in the traditional sense (input number -> output number) is impossible for higher levels. It translates the FGH expression into a known
It translates the FGH expression into a known large number notation (Conway chained arrows, BEAF, or TREE sequence comparisons).
An FGH calculator is not a tool you use to balance your checkbook. It is a conceptual (and sometimes actual) piece of software designed to compute—or at least approximate—functions that grow faster than any human intuition can follow. Building one is a journey into the foundations of computation, ordinal notations, and the very meaning of "infinity."
