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 \(f_{\omega^2}(x)\).