A 90 minute time series of high spatial resolution white-light images of solar granulation, obtained at the Swedish Vacuum Solar Tower (Observatorio del Roque de los Muchachos, La Palma), was analyzed to study how the physical properties of the granules changed with size. The observational material was corrected for global motions and for the instrumental profile, and a subsonic filter was applied. A definition of granular border was adopted using the inflection points of the intensity of the images, and the granular cells were defined as areas including, in addition to the granules, one-half of their surrounding intergranular lanes. Using time series to investigate the average behavior of solar granulation has three strong advantages: the first is the possibility of removing the acoustic waves; second, the possibility of estimating the effect of the variability of seeing on our results; and, third, the opportunity to attain high statistical significance in the analysis as a result of the large number of extracted granules (61,138). It is shown that the granules of the sample can be classified according to their mean and maximum intensities and their fractal dimension into two regimes, with diameters smaller than and larger than 1."4, respectively. A broad transition region in which both regimes coexist was found. The resolved internal brightness structure of both the granules and the intergranular lanes shows a linear increase of the number of substructures with the granular and intergranular areas. The diameters of these substructures range between our effective resolution limit (~0."3) and ~1."5, with preferential sizes at 0."65 and 0."55, respectively. Moreover, it seems that large and small granules are unevenly distributed with respect to the large-scale vertical flows. Thus smaller granules are more concentrated along downdrafts whereas larger ones preferentially occupy the updrafts. Finally, a physical scenario compatible with the existence of these two granular populations is discussed.