Imagine a machine that cuts threads on screws but forbids left-handed ones. A screw can be turned right in any way, but left is not allowed. Physicists have just found a similar rule for the tiny magnetic arrows inside certain materials.
The new rule works like this: on each pyramid of four atoms, one of the two twists of the arrows is forbidden. If three arrows are already set, the fourth is determined uniquely, and this rule turns out to be akin to turning a sphere inside out. On different lattices of such pyramids, different patterns arise: in some places there are many of them, while in others a rigid order appears.
Previously, it was unclear whether such a rule could be imposed exactly and without choosing a direction. Now this has been achieved, and the models could be useful for testing quantum computers. Although no applications are in sight yet, the very fact that a simple "forbid the left" generates so much diversity is already changing our understanding of magnetic materials.
For spin 1/2 on a single tetrahedron, 15 of the 16 possible states are zero modes, and only one state, the chiral singlet with the opposite twisting, is excluded. This means that the rule selecting chirality costs just one state out of sixteen.
The idea of local rules generating complex collective behavior echoes the concept of cellular automata in science fiction, for example in Greg Egan's novel 'Permutation City', where simple rules on a lattice create emergent structures.