User blog:GamesFan2000/Mega-Expanding Array Function (MEAF)

Taking a break from E* notation, or function, or whatever, and returning to familiar territory. Yep, I’m making ANOTHER array notation. This one is called the Mega-Expanding Array Function.

Rules
For this, we’ll be using 0 and all positive integers in a system of arrays, taking the form of A(a, b, c, ...x, y, z). Every array has a distinct value, which is determined through the following rules:

A(n) and A(n, 0)=n↑nn

A(n, m+1)=A(((...(((n, m), m), m), ...), m), m), where there are n m’s.

A(n, ...z, 0)=A(n, ...z)

A(n, ...y, z+1)=A((...((n, ...y, z), z), ...z), z), where there are (n, ...y) z’s.

Examples
A(3)=3↑33

A(4, 3)=A((((4, 2), 2), 2), 2)=A(((((((4, 1), 1), 1), 1), 2), 2), 2)=A((((((((((4, 0), 0), 0), 0), 1), 1), 1), 2), 2), 2)

A(2, 2, 2, 2)=A(((...((((2, 2, 2, 1), 1), 1), 1), ...1), 1), 1), which has (2, 2, 2) 1’s.