In exemplary implementations of this invention, a shape controller controls the shape of a bladder as the bladder inflates. The shape controller includes a first set of regions and a second set of regions. The second set of regions is more flexible than the first set of regions. The shape controller is embedded within, or adjacent to, a wall of the bladder. When the bladder is inflated, the overall shape of the bladder bends in areas adjacent to the more flexible regions of the shape controller. For example, the shape controller may comprise paper and the more flexible regions may comprise creases in the paper. Or, for example, the more flexible regions may comprise notches or indentations. In some implementations of this invention, a multi-state shape display changes shape as it inflates, with additional bumps forming as pressure in the display increases.