We are not good at judging randomness. The R Markdown document compares two figures containing a selection of dots scattered on a grid. One of the grids has a truly random scattering of dots. The other has a pattern of dots, but nevertheless, looks more random to the average observer.
VectorPosse/random_dots
This is a demonstration of random dots that don't always "look" random, and non-random dots that "look" random.