We study, by means of an atomistic toy model, the interplay of ferroelastic twin patterns and electrical polarization. Our molecular dynamics simulations reproduce polarity in straight twin walls as observed experimentally. We show, by making contact with continuum theory, that the effect is governed by linear flexoelectricity. Complex twin patterns, with very high densities of kinks and/or junctions, produce winding structures in the dipolar field, which are reminiscent of polarization vortices. By means of a "cold shearing" technique, we produce patches with high vortex densities; these unexpectedly show a net macroscopic polarization even if neither the original sample nor the applied mechanical perturbation breaks inversion symmetry by itself. These results may explain some puzzling experimental observations of "parasitic" polarity in the paraelectric phase of BaTiO3 and LaAlO3.