A polygon ringed with Yoshimura creases that folds from a flat sheet through a bowl to a flat stack the size of its centre, like a flower closing.
After the bloom patterns of Wang, Lang and Howell, 2025
A bloom pattern is a sheet that folds flat and opens out again to a sheet many times larger, ringed around a central polygon like the blades of a camera's aperture. Zhongyuan Wang, Robert Lang and Larry Howell named the family in 2025. This one is built from the Yoshimura pattern, the diamond buckles that Yoshimaru Yoshimura found in crushed cylinders: around a regular m-sided polygon, each wedge is a patch of isosceles triangles whose sharp angle is π/m, laid out exactly as their paper gives it.
Mountain folds run along the diagonals and valley folds along the rest, and every vertex keeps Kawasaki's rule, that alternate angles around it sum to a straight line, which is what lets it lie flat. Folded right down, every crease vertex lands on a corner of the central polygon. The fold you see is simulated: each triangle's edges are stiff bars, each crease a hinge pulled towards its fold, as in Ghassaei's Origami Simulator, and the sheet settles at each step.
Paper barely stretches, so each bloom folds only as far as it can without stretching more than a few per cent; the smaller ones close completely, the larger stop as a deep bowl. The crease pattern can fold too, as its creases alone. In motion the bloom opens and closes.
Behind the mathematics
Bloom patterns, 2025
Mechanical engineering student at Brigham Young University who, as an undergraduate, identified bloom patterns: origami that folds flat and opens radially from a central polygon, published with Robert Lang and Larry Howell in 2025.
Bloom patterns, 2025
American physicist and origami artist whose computational methods, from TreeMaker to circle packing, put origami design on a mathematical footing and into engineering, including folded space telescopes and the bloom patterns.
Bloom patterns, 2025
Mechanical engineer at Brigham Young University and a founder of the field of compliant mechanisms, whose lab has turned origami into deployable arrays, medical devices and the bloom patterns.
The Yoshimura pattern
Japanese engineer whose 1951 study of thin cylinders crushed along their length described the diamond buckling now called the Yoshimura pattern, published in English by NACA in 1955.
Folding for deployable structures
Japanese astrophysicist and space engineer whose Miura fold, grown from his work on the Yoshimura pattern, lets a sheet unfold in a single motion; it flew on the Space Flyer Unit's solar array in 1995.
