  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.
