The controlled folding and unfolding of maps,
space structures, wings, leaves, petals, and other
foldable laminae is potentially complicated by the
independence of individual folds; as their number increases, there is a combinatorial explosion in the number of folded possibilities. The
artificially constructed Miura-ori (1) pattern,
with a periodic array of geometrically and
elastically coupled mountain and valley folds
(Fig. 1A), circumvents this complication by
allowing the entire structure to be folded or
unfolded simultaneously. Making such a pattern is not easy, so it may be surprising to find
an elegant natural counterpart that is a few
hundred millennia old. In Fig. 1B, we show the
different stages of the opening of a hornbeam
leaf that starts life in its bud as a Miura-ori
folded pattern (2). Similar structures arise in
insect wings (3) and elsewhere in nature (4),
suggesting that these origami patterns are a
result of convergent design. This raises a question of mechanism: How might this spatial
organization of folds be brought about?