Moiré Patterns - Emergent Interference

Two identical patterns, slightly rotated → emergent interference pattern

Controls

Pattern Type

Parameters

Rotation (degrees) 5.0°

Scale difference (%) 0%

Line spacing (px) 8

Line width (px) 2

The Math

Moiré period = λ / (2 sin(θ/2))
As θ → 0, period → ∞

Spatial frequencies interfere like waves. The "beat frequency" creates the visible pattern.

Presets

Wave Interference

Moiré patterns are fundamentally a form of spatial interference—the same physics behind the double-slit experiment! When two periodic structures overlap, their spatial frequencies combine. Where they align: constructive interference (dark). Where they cancel: destructive (light).

Emergent Complexity

Neither layer contains the swirling pattern you see—it EMERGES from their interaction! This is a perfect visual metaphor for emergent phenomena in complex systems. Simple rules, layered together, create structures that aren't "in" any individual component.

Magic Angle Graphene

In 2018, physicists discovered that stacking two graphene sheets rotated by exactly 1.1° creates a moiré superlattice that becomes a SUPERCONDUCTOR! The "magic angle" creates electronic interference patterns that enable zero-resistance electricity flow.

Art, Security & Problems

Op artists like Bridget Riley deliberately create moiré for visual effects. Security holograms use moiré for anti-counterfeiting. But in printing and photography, moiré is a nuisance—causing unwanted patterns when scanning halftone images or photographing screens!