The Fast-Growing Hierarchy (FGH) is an ordinal-indexed family of functions used in mathematical logic and "googology" to classify the growth rates of extremely large numbers Online Fast-Growing Hierarchy Calculators

• F_0(n)=n+1.
• F_1(n)=F_0^(n)(n)=n + n = 2n.
• F_2(n)=F_1^(n)(n): iterate doubling n times starting at n gives n * 2^n (roughly).
• F_3 grows like tower-of-twos of height ~n.

. A high-quality calculator allows you to toggle between different standard systems (like the Wainer hierarchy). 3. Big Number Notation Translation

: While not a dedicated FGH tool, it is highly reliable for computing lower levels of the hierarchy (e.g., for finite

One evening, Mira reran an old experiment: a hierarchy representing her late mentor’s lab, collapsed after budget cuts into a sparse web. She fed the web into the Calculator and set it to simulate decades. The hybrid strategy, she discovered, allowed the lab’s surviving strands to regrow in a dozen different directions and then fold their findings into a coherent program—something the original lab had never achieved in its steady, vertical climb.