Explicit formula for $x(0)=0, x(n+1) = x(n)^2 +1$

Question

If $f(x) = \sqrt{x-1}$ and we compose $f(x)$ $k$ times, then a recursive formula for its zero, $x(k)$, is given by the recursive formula relation $x(0)=0, x(n+1) = x(n)^2 + 1$.

This is nice, but how might we find an explicit formula for $x(k)$?