We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one- and two-dimensional point placement models to illustrate possible generic behavior of these distributions. We show, numerically and analytically, that these models all lead to multifractal spatial distributions of population. Additionally, we make qualitative links between our models and the example of the Earth at Night image, showing the Earth's nighttime man-made light as seen from space. The Earth at Night data suffer from saturation of the sensing photodetectors at high brightness ("clipping"), and we account for how this influences the determined dimension spectrum of the light intensity distribution.