  For an $n\times n$ random image with independent pixels, black with
probability $p(n)$ and white with probability $1-p(n)$, the probability of
satisfying any given first-order sentence tends to 0 or 1, provided both
$p(n)n^{\frac{2}{k}}$ and $(1-p(n))n^{\frac{2}{k}}$ tend to 0 or $+\infty$, for
any integer $k$. The result is proved by computing the threshold function for
basic local sentences, and applying Gaifman's theorem.
