  We generalize Brudno's theorem of $1$-dimensional shift dynamical system to
$\mathbb{Z}^d$ (or $\mathbb{Z}_+^d$) subshifts. That is to say, in
$\mathbb{Z}^d$ (or $\mathbb{Z}^d_+$) subshift, the Kolmogorov-Sinai entropy is
equivalent to the Kolmogorov complexity density almost everywhere for an
ergodic shift-invariant measure.
