## FANDOM

10,821 Pages

Review of part 1:

$SH(x)=39^x$

$SH(N,a,x)=SH(N,a-1,SH(N,a,x-1))$

$SH(N,a,0,M)=SH(N,a-1,SH(N,a-1,a,M),M)$

$SH(0,N)=SH(N)$

(note: N,M can be nothing and 0 in the second formula is the leftmost zero.)

I repeat arguments themselves. I mean,

$SH(1/x)=SH(x,x,...(x times)...,x)$

And then,

$SH(n/x)=SH(n-1/x,x,...(x times)...,x)$

Also, this can be thought:

$SH(1/x/n)=SH(x,x,...(x times)...,x/n)$

If each slash have arrays, It must be 2D array.

Now, here is a 3D array notation:

$SH(n//m)=SH(m,m,...(ntimes)...m/m,m,...(ntimes)...m/...(ntimes).../m,m,...(ntimes)...m)$

Now it get complicated, so I will summarize my definitions.

$SH(x)=39^x$

$SH(N,a,x)=SH(N,a-1,SH(N,a,x-1))$

$SH(N,a,0,M)=SH(N,a-1,SH(N,a-1,a,M),M)$

$SH(0,N)=SH(N)$

$SH(a/b/N)=SH(a-1/b,b,...(btimes)...,b/N)$

$SH(N,a/0/M)=SH(N,a-1/SH(N,a-1/a/M)/M)$

I define a phrase n-dimensional array of m (nDm) : it is a notation of m's filled with n-dimensional cube with a size of n.

$SH(N/^k a/^n b)=SH(N/^k a-1/^n (n-1Db))$

$SH(N,a/^k 0/^n b)=SH(N,a-1/^k SH(N,a-1/^k a/^n b)/^n b)$