User blog comment:MilkyWay90/Not-Registered Users, tell your Googology ideas in the comments/@comment-2601:142:2:EC49:2866:7BBA:96EE:D0B9-20180821120219

Here's my idea! This is a 3+ variable FGH-inspired function, ( x,y(z) ) Enjoy! ;D

(Also, if there are multiple arrays in the brackets, then decompose the right-most array and ignore the others.)

Rule 1: 0,0(x) = x+1

Rule 2: x,0(y) = (x-1),y], [(x-2),y], [(x-2),y]..., [0,y(y)

Rule 3: x,y(z) = x,(y-1)], [x,(y-1)], [x,(y-1)]..., [x,(y-1)(z) w/ z [x,(y-1)]s

Fairly simple, but to make sure you get it, here's the decompisition of 2,0(2).

2,0(2)

Invoking rule 2 on the 2,0...

1,2], [0,2(2)

Invoking rule 3 on the 0,2...

1,2], [0,1], [0,1(2)

Invoking rule 3 on the 0,1...

1,2], [0,1], [0,0], [0,0(2)

Invoking rule 1 twice on the 0,0s...

1,2], [0,1(4)

Invoking rule 3 on the 0,1...

1,2], [0,0], [0,0], [0,0], [0,0(4)

Invoking rule 1 four times on the 0,0s...

1,2(8)

I could go on, but I feel like you get the idea at this point. (If you're curious, [2,0](2) decomposes to be equal to fw+2(8) in the FGH)

I shall now define O(x,y,z) as x,y(z) (Here's where I point out that O(2,0,2) dwarfs Graham's number.)

And I define OX(n) as O(n,n,n).

How strong is OX(n)?