Logarithm of power spectrum, normalised histogram, and colour maps of the vertical outward bolometric intensity I at the top of the atmosphere for the G2V (top row), K0V (middle), and M2V (bottom) stars. Left column: logarithm of the time averaged radial spatial power spectrum of the intensity versus the logarithm of the radial spatial frequency f. Second column: Logarithm of the relative frequency f of the normalised histogram of the intensity for the complete time series. In both the left and second columns, dark solid and light dashed lines indicate upflos and downflows, respectively; blue thick and red thin lines indicate SSD and HD runs, respectively. Third and right columns: colour maps of the intensity of the last snapshot of the HD (third column) and SSD (right) time series. Red circles show the location of magnetic bright points produced by flux concentrations (see Fig. 6).