Fast Growing Hierarchy Calculator

This piece covers the mathematical foundations, the engineering challenges of building such a calculator, and provides a working code implementation for the computable levels of the hierarchy.

Overflow handling:

• Example: ( f_3(2) ) expands to ( f_2(f_2(2)) ).

• Plot f_α(n) for n = 1..5 (log scale).
• Compare with other ordinals: e.g., overlay f_ω(n) vs f_ω+1(n).