The Busy Beaver Function

The "Busy Beaver" mathematical function, coined by Tiber Rado' in 1962, demonstrates the concept of a Turing Machine. To show how the function works in a simplified form, Numberphile and Computerphile show this rather neurotic little beaver-shaped droid who's both scared of the dark and conscious of its energy consumption (n=2), so it will work tirelessly until the amount of lights in a hall with infinite rooms is JUST the right amount where all of its needs are satisfied. This keeps going even if the amount of different compulsions it can get (n) is 10^100 or larger.

Example of:
Busy Beaver