Aggregation patterns in systems composed of few magnetic particles

In this work, we study the aggregation patterns that we observe in systems composed of two and three magnetic particles interacting magnetically and via solid-solid contact in two-dimensions. We use a discrete element method to take into account solid-solid interactions between pairs of particles. The particles are initially separated and, in the case of three particles, placed in the vertex of an equilateral triangle, and then are allowed to evolve for a given period of time. The final configurations are identified and associated to different levels of magnetic potential energy. We construct bifurcation diagrams for both cases by considering several initial conditions of the orientation of the magnetic dipole and identifying the final state configurations. In both cases, the majority of the final configurations is the aggregation of the particles in chains, but a non-negligible number of initial configurations leads to complete dispersion of the particles. Finally, we explore in more detail the surprising fractal nature of the bifurcation diagram.