Overlap two regular grids and something extraordinary appears — a third pattern, larger and more complex than either, that exists only in the interference between them.
Moiré patterns (from the French moiré, meaning "watered") are emergent interference patterns produced when two periodic structures overlap at slightly different angles or scales. They appear in screen doors, silk fabric, TV screens filming other screens, and — remarkably — in the physics of twisted graphene that may unlock room-temperature superconductivity.
Every time you've looked through two chain-link fences, worn a striped shirt on TV (shimmering artifacts), or noticed strange swirls when photographing a screen — that's moiré. It's also why banknotes use intricate line patterns: moiré effects from photocopying are an anti-counterfeiting measure.
In 2018, MIT physicist Pablo Jarillo-Herrero discovered that stacking two sheets of graphene (single-atom carbon layers) and twisting them to exactly 1.1° produces a moiré superlattice that becomes superconducting at low temperatures. The pattern of interference between the two atomic lattices creates new electronic properties that neither sheet has alone.
This discovery — called "twistronics" — has spawned an entire field. The moiré pattern isn't just visual; it's a physical structure that traps and channels electrons in ways that could revolutionize computing and energy.
"The moiré pattern is not in either grid. It's in the relationship between them. That's what makes it profound — it's pure emergence." — Philip Ball, science writer
Two overlapping gratings with spacings d₁ and d₂ at angle θ produce a moiré with spacing: D = d / (2·sin(θ/2)) for identical gratings. As the angle approaches zero, the moiré wavelength approaches infinity. This is why even tiny angular differences produce dramatic large-scale patterns — the math amplifies the subtle.
This amplification property makes moiré patterns extraordinarily useful for precision measurement. Engineers use them to detect surface deformations smaller than a wavelength of light, and semiconductor manufacturers use them to align lithography masks to nanometer precision.