  In the present work, a geometrical method to generate a two dimensional
random walk by means of a bidimensional Cellular Automaton is presented. We
illustrate it by means of Conway's Game of Life with periodical borders, with a
large lattice of 3000 x 3000 cells. The obtained random walk is of character
anomalous, and its projection to a one dimensional random walk is analyzed,
showing that it presents some statistical properties similar to the so-called
stylized facts observed in financial time series. We consider that the
procedure presented here is important not only because of its simplicity, but
also because it could help us to understand and shed light on the stylized
facts formation mechanism.
