Forum:Help with stating algorithm

I am playing around with an idea, and would like help with how to state a part of the algorithm as a mathmatical function. It's been a long time since I had a math class, so excuse any confusion but please clarify and correct. This is probably pretty trivial to answer one way or another.

The part of the algorithm I want help with  is:

FISN(x) should be defined as a function that has x total nested levels of: the number x seperated by x conway chained arrows with the result iterated back into the preceding steps x times.

To help clarify what I am trying to state here are some examples.

FISN(0) = null

[0 >'s in 0 nested levels iterated 0 times]

FISN(1) = 1 > 1

[ 1's seperated by one >'s in one nested level(s) iterated one times]

FISN(2) = Iteration 1: ((2 > 2 > 2) >  (2 > 2 > 2) >  (2 > 2 > 2)) = A   So that's two >'s nested in two >'s filled with 2's.


 * Iteration 2: (... (A1 >  A 2  > ...  >  A A-1 ) > ( A1 >  A 2  > ...  >  A A-1 )... ) = x  Where there are A nested levels of A number of >'s seporating the number A.

[2's seperated by two >'s in two nested levels with the those steps iterated a total of two times. Thus the answer from iteration one is the x for iteration two. *NOTE that includes defining the new level of nesting]

FISN(3)  Iteration 1: (((3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) >  (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3)) > ( (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) >  (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3)) >  ( (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) >  (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3))  > ( (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3) >  (3 > 3 > 3 > 3) > (3 > 3 > 3 > 3))) = A    Where there are 3's seporated by three >'s nested three deep in sets of three > operators.


 * Iteration 2:  (... (A1 >  A 2  > ...  >  A A+1 ) > ( A1 >  A 2  > ...  >  A A+1 )... ) = B  Where there are A nested levels of A number of >'s seporating the number A.


 * Iteration 3:  (... (B1 > B 2  > ...  > B B+1 ) > (B 1 > B 2  > ...  > B B+1 )... )   Where there are B nested levels of B number of >'s seporating the number B.


 * [3's seperated by three >'s in three nested levels with those steps iterated a total of three times. Thus the answer from iteration one is the x for iteration 2, and the answer from iteration two is the x for iteration 3]