Fig. 1.

Encoding information into magnetic panels to generate specific interactions. (A) Four unique magnetically patterned layers are constructed by using a $2\times 2$ array of magnets with different orientations (top and side views). The magnetically patterned layers are arbitrarily colored black, green, blue, and red according to their dipole patterns. Spacers are glued to the 2 faces of the magnetically patterned layer to make a panel. (B) Magnetic force between 2 magnetically patterned layers of the same pattern at the optimal binding orientation (sketch in Inset) versus the center-to-center layer separation. Here, we normalize the separation by the lateral dipole separation within a magnetically patterned layer. Solid lines are experimental measurements, and dashed lines are results from analytic calculations in which interactions between any 2 pairs of magnets that are not in the same magnetically patterned layer are considered. We glue spacers onto the magnetically patterned layers to further enhance the selectivity of the panel interactions. These spacers create a steric repulsion at a surface separation corresponding to the vertical dashed line. (C) Plot of the range for spontaneous binding (normalized by the dipole separation within a panel) versus $\mathrm{\Gamma }$, the shaking acceleration normalized by $g$. Data are obtained by placing panels face to face, releasing them and determining if they spontaneously bind. (D) Schematic illustrating the interactions between panels of different orientations (top left) and dipole patterns (bottom right). (E) Theoretical calculation of the ground-state binding energy between any 2 panels. (F) Theoretical calculation of the binding-energy landscape of 2 panels of the same dipole pattern as a function of the lateral separation normalized by the dipole separation within a panel. The globally optimal ground state occurs when the panels are face to face with no separation. In addition, we find the metastable states of green, blue, and red panels. Data are obtained by orienting panels face to face with the separation equal to twice the spacer thickness. Energies are calculated by displacing the panels laterally, keeping the panels parallel, and optimizing their relative orientation in the panel plane.