Algorithmic Function

This is a function that use an algorithm produces fairly big numbers. 
== #(n) ==
To obtain the output : choose a integer n superior to 1 and follow the first step. 
Step a (for a<n) : Repeat n times step a+1 
Step n : Set n to n+1.  
The end result is written as #(n). This may seem weak, but if we just change step n to : ”Repeat n times step 1.0” and define step 1.0 as “Set n to n+1”, we already have something faster than the graham function ! . Its just f_ω(n+1). Now we can define #_1(n) and #_x(n).
== #_1(n) ==
Step a (for a<n) : Repeat n times step a+1 
Step n : Repeat n times step 1.0 
Step a.b : (for a and b <n)
Repeat n times step a.b+1 Step a.n (for a<n):	 Repeat n times step a+1.0 
Step n.0 : Add 1 to n 
#_x(n) is an extension of #_1(n) that goes up to step n.0.0.0.0.0.0… with x zeroes. 
The Supreme Algorithmic Function is #_n(n) and has a growth rate of f_(ω^ω) f_ω(n^n) using FGH.
== #_Δ(n) ==
Δ_1(x) is step x.0.0.0.0... with x terms.
You can think of #(n) as simply a column of steps, #_1(n) as a collection of any columns : a plane of steps, #_2(n) a cube of steps, and #_x(n) as a (x+1)-cube.
Now, you can imagine step Δ_1(x) as x x-cubes, Δ_1(x,0) as x columns of x-cubes, Δ_1(x,0,0) as x cubes of x-cubes (x cubes = x 3 dimensional cubes; x-cubes = some number of x-dimensional cubes) , etc.
Δ_2(x) is x x-cubes of x-cubes. 
Δ_3(x) is x x-cubes of x-cubes of x-cubes.
Etc.
The Supreme Metacube Function (#_Δ(n)) is a function that uses the algorithm up to Δ_n(n) and has a growth rate of f_(epsilon(0)) f_w(n^^n)
== #_ω(n) ==
We can still define steps that come after !
ω_1(n) is n columns/lines of "n-cube of n-cubes of n-cubes of n-cubes..."
ω_1(n,0) is n planes
ω_1(n,0,0) is n cubes
etc.
ω_2(x) is n n-cubes of n-cubes.
ω_3(x) is n n-cubes of n-cubes of n-cubes.
Etc.
The Supreme Metametacube Function (#_ω(n)) is a function that uses the algorithm up to ω_n(n).
Growth : f_w(n^^n^^n)
== #_Ω(n) ==
You can probably see the pattern between #_Δ(n) and #_ω(n). We can continue the pattern and use the hypercube thingy in the index itself !! This gets us to the last extension of the function (for now) : #_Ω(n). Basically : its a metametametameta... (the "meta" form a metametametameta...(the "meta" form a metametametameta...(the "meta" form a metametametameta...(the "meta" form a metametametameta...(...cube)cube)cube)cube)...cube.
I call it : the hypermeta-cube function
Growth rate : f_w(n^^^n) Category:Math functions