Geometry-driven hyperuniformity via Lloyd iterations

A browser-scale demonstrator for comparing standard and perturbed Lloyd relaxation. The left panel shows points and Voronoi cells; the right panel tracks scalar metrics over iteration.

Number of points

Initial condition ?

Constraint / boundary ?

Voronoi colour mode ?

Seed ?

Animation speed ?

Perturbation schedule ?

Amplitude, fraction of mean spacing ?

Perturbed fraction ?

Perturbation distribution ?

Perturbation location ?

Local radius / strip width ?

Window start ?

Window end ?

Perturb every k steps ?

Impulse step ?

center-of-mass correction for perturbation displacements ?

This keeps the selected perturbation field from adding a net translation.

n-sided cell: n=5 n=6 n=7 other n

Hexatic phase: -ππ

step0

energy-

|ψ_6| mean-

S low-k-

The demo uses D3 Voronoi cells and is intended for interactive intuition. Use the Python executable for publication-grade periodic calculations with freud-analysis.

Total quantizer energy?

Mean-square displacement?

Mean hexatic-order modulus?

linear

S(k) structure factor for low k?

log-log

5/6/7-sided cell fractions?

linear

f5f6f7