To leave or to stay (and what season tickets and club memberships have to do with it)? A qualitative study on the exit of German soccer supporters.

Thornton, I. M., Zdravković, S., Riga, A., Todorović, D. (2026). Dynamic illusory waves generated by relative motion in periodic displays. , (4), 1–6. The purpose of this brief report is to introduce and make available an online interactive tool where readers can create and manipulate what we are calling ‘dynamic illusory waves’. As illustrated in , the appeal of the display is the manner in which a very salient and compelling illusory surface can be generated from the combination of two relatively simple physical components: a shape with a sinewave-modulated contour and a regular ‘pinstripe’ grating. The exact form taken by the dynamic illusory wave (diwa) is primarily determined by the spatial frequency ratio of the two physical elements. Local phase differences at points of intersection define a subjective contour, which in turn gives rise to an illusory surface. When relative motion is added – either by temporally modulating the borders of the physical shape or by drifting the grating – this appears to amplify the illusion, producing a non-rigidly deforming illusory wave, which typically appears as a transparent occluding surface. Dynamic Illusory Waves (diwas). https://maltacogsci.org/diwa/diwa_movie1.html