This picture shows a collineation (i.e. an incidence-preserving bijection) of the affine plane over the field K=Q(2){\displaystyle K=\mathbb {Q} ({\sqrt {2}})}. This collineation is not affine, since it fixes three a triangle (OE1E2){\displaystyle (OE_{1}E_{2})} of the plane but is not the identity though: The red points are reflected at the point O. This semilinear mapping of the plane is induced by the nontrivial automorphism of the field K.
Own work
KlioKlein