This chapter is dedicated to special applications of techniques which could be called “discrete random deviations”. With this term is meant the use of random deviations [real numbers in the open interval (0 < r < 1)] applied in the one- or n-dimensional case to simulate events occurring in n-dimensional space. Examples of application are given for several variants of Diffusion Limited Accretion (DLA), which consists in diffusion of small particles carried by a fluid and in formations of aggregates of particles upon impingement with the growing aggregates. The phenomenon occurs in soot formation, in clusters of aerosol particles in the atmosphere, in dendrites formed by mineralization, and the like. Numerical simulations show formation of branches in a confined quadrant of the definition domain; grow of on dendrites in an unbound domain and geodes growth un spherical geometry.