Eisenstein Integers

Exact hexagonal arithmetic. Zero drift after 10,000 rotations.

IEEE 754 Float

Rotations: 0

Drift: 0.000px

Eisenstein E12

Rotations: 0

Drift: 0.000px

Angle: 1.0° Speed:

Both points start at (1, 0) and rotate by the same angle each step. Float accumulates error. E12 doesn't.

Explore the Hexagonal Lattice

Click any point. Hover to see D6 symmetries. Scroll to zoom. Drag to pan.

E12: —

Norm: —

Cartesian: —

Angle: —

D6 orbit: —

Eisenstein Playground

Snap angles, compute norms, explore rotations — all in your browser.

Snap angle to E12

Enter an angle and press Snap

Compute E12 properties

Enter E12 coordinates

Drift comparison

Enter rotation count

HexDisk radius

3N²+3N+1 points

Float vs Eisenstein — Side by Side

Same operation, different math. See the drift accumulate in real-time.

Float (IEEE 754)

Click "Run Both" to start

Eisenstein E12

Click "Run Both" to start

Rotations: Angle: rad

Rust Quickstart

// Cargo.toml: eisenstein = "0.3"
use eisenstein::{E12, HexDisk};

let z = E12::new(-5, 3);
assert_eq!(z.norm(), 49);  // a²-ab+b² = 25+15+9

let dir = E12::snap_from_angle(0.0);
let disk = HexDisk::radius(36); // 3,997 vertices

crates.io · GitHub · Errata · CUDA benchmarks