I've been looking for a solid square (non-pourus) that can expand to 12x it's size and back again. This needs to grow and shrink on only the x and y axis, the z doesn't matter whether it grows or not. The expansion and retraction needs to be done smoothly or in small increments and equally (not x first then y or vice versa). This process to be done more than once. I was thinking an elastic material but some materials stay permanently stretched once crossing a certain point, staying too long, or show marks of stretching when restored (like a balloon after someone pulls it). Prefer it to be done mechanically. Most of the heat-based ideas i've found either don't change to the size requirements or are one-time solutions.
Yes: a crumpled piece of paper.
Many origami tessellations can stretch to many times their original size reversibly. There are limitations of course: how thin the paper material is, how much it tolerates damage in the creases and ultimately how well one can fold. Other than that you can get quite impressive ratio between the folded/unfolded states. The "Miura-ori" is quite the star in that domain. Here how it looks.