Fish number 2

Fish number 2 (F2), is a number defined by Japanese googologist Fish in 2002. Its base is the same as in Fish number 1:
 * \(S_1(0,y) = y+1\)
 * \(S_z(0,y) = S_{z-1}(y,y)\) for \(z ≥ 1\)
 * \(S_z(x,0) = S_z(x - 1,1)\)
 * \(S_z(x,y) = S_z(x - 1,S_z(x,y - 1))\)

The function \(S_x(x,x)\) grows about as fast as \(f_{\omega^2}(x)\).

After that, we get a SS map. We have a function \(SS(3,x+1,S)\) which expands to \(S_{x+1}(3,3)\). Then we have an S map over that, which iterates the function \(x+1\). If we have an SS map over that, we get a function with growth rate \(f_{\omega^22}(x)\). Fish number 2 is defined as \(SS^{63}(3,x+1,S)\)