Experimental flat-folding and crumpling data were performed on 10 cm by 10 cm sheets of 0.05-mm-thick Mylar. Flat folds were performed successively at random, without allowing the paper to unfold between successive creases. Crumpled sheets were obtained by first rolling the sheet into a 3-cm-diameter cylinder and then applying axial compression to a specified depth between 7.5 and 55 mm. Sheets were successively crumpled between 4 and 24 times.

To image the experimental crease network, crumpled/flat-folded sheets were opened up, and their height profile was scanned using a home-built laser profilometer. The mean curvature map was calculated by differentiating the height profile and then denoised using a custom Radon-based denoiser (the implementation details of which are given in section S1). A total of 506 scans were collected from 31 different experiments.

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