Interactive interference fringe visualization from overlapping periodic patterns
When two layers of periodic patterns overlap with a slight angular difference or displacement, wave superposition creates visible beat patterns called Moire fringes. These emerge from the mathematical product of two periodic functions, where frequency differences produce low-frequency interference structures.
Mathematically, when two patterns f(x,y) and g(x,y) overlap, their product reveals interference terms. If f has spatial frequency f1 and g has frequency f2, the resulting pattern contains both f1+f2 and |f1-f2| components. The low-frequency difference term is the visible Moire pattern.
Moire patterns have wide applications: printing anti-counterfeiting, precision measurement (strain gauges), optical alignment in semiconductor lithography, surface quality inspection, and artistic design. They also demonstrate fundamental wave interference principles.
Drag on the canvas to interactively change the rotation angle (horizontal) and displacement (vertical) of Layer 2. Use the sliders for precise control. Try different pattern combinations to discover the rich variety of Moire interference effects.