Study Nº 195 · Op-art / Interference
Two identical gratings share one field. One of them turns — slower than a minute hand, by an angle your eye cannot resolve. The interference does the shouting: bands two hundred pixels deep sweep the frame, magnifying a rotation you cannot see into geometry you cannot miss.
Two combs of identical teeth. One is turning. Watch the horizontal bands breathe.
The magnifier
D = p2·sin(θ/2)
fringe period = pitch ÷ twice the sine of half the angle · for small θ, D ≈ p/θ
Moiré is a vernier without numbers. Overlay two gratings of pitch p and rotate one by θ: the beat between them has a period of roughly p divided by the angle. Small divisor, huge quotient. A two-degree turn — about the width of a clock tick — multiplies an 8-pixel pitch into a 229-pixel band. The pattern is a lever with no moving parts: it takes a difference too small to see and pays it out as geometry too big to ignore.
Metrologists read fractions of an arc-second this way. Halftone printers fear it — two misregistered screens beat into blotches. Bridget Riley hung its nerve-endings on gallery walls and let the retina do the arithmetic.
| rotation θ | fringe D | gain D÷p |
|---|---|---|
| 1° | 57.3 p | ×57.3 |
| 2° | 28.6 p | ×28.6 |
| 4° | 14.3 p | ×14.3 |
| 8° | 7.2 p | ×7.2 |
Two combs of 3.8-pixel teeth at pitch 8. Turn one by two degrees — smaller than the gap between minute marks on a wristwatch — and horizontal bands the height of your hand roll through the field. Divide pitch by angle: the bands are the quotient.
532 strokes · one secret rotation
Two bullseyes, centres a knuckle apart. Their beat draws hyperbolas — the same curves two pebbles cast on a still pond, because shifted ring gratings and interfering point sources are one mathematics wearing two inks.
240 circles · Young's experiment in dry ink
Two dot lattices at a small twist beat into a third, coarser lattice — magnified by 1/θ. Stack two sheets of graphene at 1.1° and this same geometry turns carbon into a superconductor. Here it merely turns a page into a shimmer.
260 dotted rows · the magic-angle toy
Provenance
Moiré came into English through French mohair — watered silk, pressed between rollers so its own weave interferes with itself and pours light like a tide. The printers borrowed the word as a curse, the physicists as an instrument, the op-artists of the 1960s as a medium: Riley, Vasarely, Soto, hanging quiet geometry that refuses to sit still.
Every mark on this page is drawn geometry — 266 strokes per line grating, 120 circles per bullseye, 130 dotted rows per lattice, duplicated once and turned. There is no photograph of a moiré here. There is only the moiré.