  The continuous tetrational function ${^x}r=\tau(r,x)$, the unique solution of
equation $\tau(r,x)=r^{\tau(r,x-1)}$ and its differential equation $\tau'(r,x)
=q \tau(r,x) \tau'(r,x-1)$, is given explicitly as ${^x}r=\exp_{r}^{\lfloor x
\rfloor+1}[\{x\}]_q$, where $x$ is a real variable called height, $r$ is a real
constant called base, $\{x\}=x-\lfloor x \rfloor$ is the sawtooth function,
$\lfloor x \rfloor$ is the floor function of $x$, and
$[\{x\}]_q=(q^{\{x\}}-1)/(q-1)$ is a q-analog of $\{x\}$ with $q=\ln r$,
respectively. Though ${^x}r$ is continuous at every point in the real $r-x$
plane, extensions to complex heights and bases have limited domains. The base
$r$ can be extended to the complex plane if and only if $x\in \mathbb{Z}$. On
the other hand, the height $x$ can be extended to the complex plane at
$\Re(x)\notin \mathbb{Z}$. Therefore $r$ and $x$ in ${^x}r$ cannot be complex
values simultaneously. Tetrational laws are derived based on the explicit
formula of ${^x}r$.
