Magnetic beads attract each other forming chains. We pushed such chains into an inclined Hele-Shaw cell and discovered that they spontaneously form self-similar patterns. Depending on the angle of inclination of the cell, two completely different situations emerge, namely, above the static friction angle the patterns resemble the stacking of a rope and below they look similar to a fortress from above. Moreover, locally the first pattern forms a square lattice, while the second pattern exhibits triangular symmetry. For both patterns the size distributions of enclosed areas follow power laws. We characterize the morphological transition between the two patterns experimentally and numerically and explain the change in polarization as a competition between friction-induced buckling and gravity.

Magnetic beads attract each other forming rather stable chains. We consider such chains formed by magnetic beads and push them into a Hele-Shaw cell either from the boundary or from the center. When such a chain is pushed into a cavity, it bends and folds spontaneously forming interesting unreported patterns. These patterns are self-similar and an effective fractal dimension can be defined. As found experimentally and with numerical simulations, the numbers of beads, loops and contacts follow power laws as a function of packing fraction and, depending on the injection procedure, even energetically less favorable triangular configurations can be stabilized.