A compilation of extremely fast-growing functions. Most of them were defined by professionals but some are personal creations. In the spirit of busy beavers, each function has been written as short and condensed as possible.
The top method is a helper function that can be used to view a function's calculations step by step.
The name of each function/notation is provided, as well as its strength in the fast-growing hierarchy and character length. Each program is sorted first by its growth rate, followed by its length.
The naga function is still being prototyped. It is an attempt at extending hydras to higher levels; for example, KP hydras are level 1 and Buchholz hydras are level 2.
Ackermann Function - https://en.m.wikipedia.org/wiki/Ackermann_function
Fast-Growing Hierarchy - https://en.m.wikipedia.org/wiki/Fast-growing_hierarchy
Hyperoperators - https://en.m.wikipedia.org/wiki/Hyperoperation
Friedmann's Vector Reduction Problem - https://googology.wikia.org/wiki/Friedman's_vector_reduction_problem
Laver Tables - https://en.m.wikipedia.org/wiki/Laver_table
Conway's Chained Arrow Notation - https://en.m.wikipedia.org/wiki/Conway_chained_arrow_notation
Taro's Multivariable Ackermann Function - https://googology.wikia.org/wiki/Taro's_multivariable_Ackermann_function
Bowers Exploding Array Function - https://googology.wikia.org/wiki/Bowers_Exploding_Array_Function
Block Subsequence Theorem - https://googology.wikia.org/wiki/Block_subsequence_theorem
Fusible Numbers - https://googology.wikia.org/wiki/Fusible_number
Kirby-Paris Hydra - https://googology.wikia.org/wiki/Kirby-Paris_hydra
Beklemishev Worm -https://googology.wikia.org/wiki/Beklemishev's_worms
Goodstein Function - https://en.m.wikipedia.org/wiki/Goodstein%27s_theorem
Buchholz Hydra - https://googology.wikia.org/wiki/Buchholz_hydra