User blog:Gonz0TheGreatt/New Googological Function

Hey guys,

I'm a new user, and I thought of a new function. After I thought of it, I found someone else had defined the exact same one (with a different name obviously), but I also defined some extensions to it. I call it the Zilla function.

n-zilla is defined as

$$2 \uparrow ^{n} 3$$. It could alternatively be defined as $$2 \uparrow ^{n-1} 4$$, or as $$2 \uparrow ^{n-2} (n-1) \text{-zilla}$$ . I found out that apparently this function was used to define a smaller version of Graham's number, but then Graham made a bigger number that was easier to describe (I still like this function though). The first few values of zilla are: 0-zilla = 6. 1-zilla = 8. 2-zilla = 16. 3-zilla = 65536. 4-zilla = $$2 \uparrow \uparrow 65536 > \text{googol}$$ 5-zilla = $$2 \uparrow \uparrow \uparrow (2 \uparrow \uparrow 65536)$$.

I define n-bizilla as n-zilla-zilla (so 0-bizilla = 6-zilla, 1-bizilla = 8-zilla, etc.). Trizilla, tetrazilla, etc. are defined similarly.

n-superzilla is defined as n followed by n zillas, so 0-superzilla = 0, 1-superzilla = 1-zilla = 8, 2-superzilla = 2-bizilla = 16-zilla, etc. n-duperzilla is n followed by n-zilla zillas, so 0-duperzilla = 0-hexazilla, 1-duperzilla = 1-octazilla, etc. Truperzilla, quadruperzilla, and so on would be extensions of duperzilla.

I like this function because all of its outputs are powers of 2, it grows very fast, and it can be defined several different ways. I was wondering what other people thought of it.