Maps of bolometric intensity and vertical magnetic field representative of the three simulation phases. The time instants of the bolometric intensity during phases 1 (first column), 2 (second column), and 3 (third column) are normalized to their respective mean intensities. The fourth column displays the vertical magnetic field at z = 0 during phase 3 at the same time instant as for the third column. The rows (from top to bottom) correspond to the spectral types K8V, K2V, G2V, and F5V. The red arrows in the K2V model indicate non-magnetic bright points, whereas the red contours in the third column denote the MBFs detected by the algorithm (see Sect. 5.3 and Appendix B).