1 - Galton board

Dropping a set of beads on a board with evenly distributed pegs results in a binomial distribution. Is it possible to generate other kinds of distributions by varying some parameters (pegs size, pegs distribution, bead format, etc.)? Is it possible to achieve a distribution that does not obey the central limit theorem in an i.i.d. scenario? What happens to the distribution when one makes the board vibrate?