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Moiré Studio

Three layered prime-fields. Each layer plots a sequence (primes / naturals / composites / twin primes / semiprimes) through some 2D map (Ulam / Sacks / Vogel / log-polar / mod-grid). Per-layer color, opacity, rotation, scale. Try the presets first — they're tuned to make moiré obvious — then twist sliders to discover your own interference patterns.

Global

N max 2000

blend mode

dot size 1.5

Layer 1

source

map

rot 0°

scale 1.00

opacity 0.85

color

Layer 2

source

map

rot 8°

scale 1.00

opacity 0.85

color

Layer 3

source

map

rot -8°

scale 1.00

opacity 0.7

color

how to use this

Default: primes-on-sacks (purple) + primes-on-vogel (gold) at 8° offset, with lighter blend. Drag Layer 2's rotation slowly — somewhere between 0° and 30° you'll see a lock-in where the two spiral systems form star patterns or radial spokes. Those are resonances: angles where the Sacks and Vogel mappings happen to send many primes to nearby positions.

Try the multiply blend: only pixels lit by both layers show up, surfacing the rare coincidences. Difference highlights the XOR. Color burn reveals low-frequency density variations. The Layer 3 (mod-grid, green) defaults off — turn it on for an orthogonal residue-class view of the same primes.