RESEARCH / FIELD STUDY 01 / SPHERICAL SAMPLING

SAME N

Same count. Different claims.

Three ways to place 1,536 points on one sphere: seeded pseudorandom draws, an equal-area Sobol prefix, and a fixed spherical Fibonacci lattice. The count stays fixed so the methods can be inspected—without pretending they make the same promise.

Status: In development
Count: N = 1,536
Methods: Random / Sobol / Fibonacci
Pairs checked: 1,178,880

Fibonacci sphere and equal-area disk, 1536 sites — PLATE / 01
Fibonacci shown. Low spacing variation is one property, not an overall ranking.
COMPUTED SPECIMEN—NOT AN EXHIBIT CAPTURE

01 / THREE LABELS

One count. Three bounded promises.

Every method places exactly 1,536 points on the same unit sphere. The count and radius hold still; the construction changes. Each label names what that construction approximates—and stops there.

Random / independent-draw model: Mulberry32 gives a deterministic pseudorandom approximation to independent uniform draws. Clumps and gaps are expected. Reproducible, not physical randomness.
Sobol / prefix coverage: The canonical, unscrambled 2D Sobol sequence, mapped to the sphere with an equal-area transform. The exhibit’s figure plate exposes its nested 128- and 512-point prefixes.
Fibonacci / fixed instrument: A fixed-size spherical lattice built on the golden angle. It depends on the chosen N and is not presented as a nested prefix.

02 / ONE STATISTIC

A local spacing statistic, not a ranking.

NN CV is the population coefficient of variation of each point’s nearest-neighbor chord distance. For N = 1,536, all 1,178,880 unordered pairs are checked—no spatial-hash approximation. A lower value means more uniform nearest-neighbor spacing for this point set. It does not decide which method is best.

03 / ENTER THE EXHIBIT

Switch the method. Keep the count.

Select Random, Sobol, or Fibonacci; toggle Spacing and Order; drag to turn the sphere. The exhibit draws with WebGL2 and falls back to Canvas2D without changing the data; both require JavaScript. This folio’s plate, text, and destinations remain available without JavaScript.