  We define a notion of isotropic surfaces in $\mathbb{O}$, i.e. on which some
canonical symplectic forms vanish. Using the cross-product in $\mathbb{O}$ we
define a map $\rho\colon Gr\_2(\mathbb{O})\to S^6$ from the Grassmannian of
$\mathbb{O}$ to $S^6$. This allows us to associate to each surface $\Sigma$ of
$\mathbb{O}$ a function $\rho\_{\Sigma}\colon \Sigma\to S^6$. Then we show that
the isotropic surfaces in $\mathbb{O}$ such that $\rho\_{\Sigma}$ is harmonic
are solutions of a completely integrable system. Using loop groups we construct
a Weierstrass type representation of these surfaces. By restriction to $
\mathbb{H}\subset\mathbb{O}$ we obtain as a particular case the Hamiltonian
Stationary Lagrangian surfaces of $\mathbb{R}^4$, and by restriction to
$\text{Im}(\mathbb{H})$ we obtain the CMC surfaces of $\mathbb{R}^3$.
