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Let $A_{\varphi}$ denote the matrix of rotation with angle $\varphi$ of theEuclidean plane, FLOOR the function, which rounds a real point to the nearestlattice point down on the left and ROUND the function for rounding off a vectorto the nearest node of the lattice. We prove under the natural assumption$\varphi\not= k\frac{\pi}{2}$ that the functions $FLOOR \circ A_{\varphi}$ and$ROUND \circ A_{\varphi}$ are neither surjective nor injective. More preciselywe prove lower and upper estimates for the size of the sets of lattice points,which are the image of two lattice points as well as of lattice points, whichhave no preimages. It turns out that the density of that sets are positiveexcept when $\sin \varphi \not= \pm \cos \varphi + r, r\in \mathbb{Q}$.

Rotation on the digital plane