Particle flocculation plays a major role in water treatment processes. In flocculation kinetics models it is usually assumed that spherical particles collide and form spherical aggregates. Real aggregates, however, are of irregular shapes and can be considered as fractal objects. The structure of fractal objects can be described by a fractal dimension number that plays an important role in aggregation kinetics. Two-dimensional computer simulations of particle aggregation are carried out in this work to directly observe the evolution of floc size and to determine their fractal dimension. The computer program developed in this study simulates random particle motion as well as cluster growth. The simulation results are visualized using Java programming language. The fractal dimension of the simulated clusters is determined based on the linear relationship between log-(mass of clusters) and log-(radius of clusters). Primary forces acting on individual particles, including van der Waals, electrostatic, magnetic dipole, and hydrodynamic interparticle forces, are examined to determine the collision efficiency at different collision angles, as well as the structure of the aggregates. The effect of magnetic dipole forces on the fractal dimension and chain formation is examined. It is shown that when the magnetic dipole force is of the same magnitude as the double-layer force within a narrow range of zeta potential values, one-dimensional or two-dimensional clusters may be obtained.