Algebraic Colored Lattice Field

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Square-free integer D

Field mode

K frequencies: 3

Frequency scale α: 0.080

Amplitude ε: 0.30

Grid size: 256

Upsample (grid sampling): 1×

Zoom granularity: 1.100

Color map

2D color map (hue ⊗ value)

Color cycling speed: 0.00

Seed (phase offset): 0

Integer offset: 0, 0

Autocorrelation walk

no vectors

Walk speed: 2.0 steps/s

About

Each lattice site x ∈ ℤ² is assigned an algebraic displacement η(x) = a(x) + b(x)√D built from a sum of K incommensurate algebraic gratings. The visualization shows the magnitude of this deterministic, aperiodic field.

Lower D values and small α yield long-range moiré-like interference reminiscent of Penrose patterns, constrained to the square lattice.

Drag to pan and scroll to zoom into the rational lattice. Use Reset view to return to the origin.