About

Vexillology - the study of flags - follows strict compositional rules. A flag that violates the rule of tincture (metal on metal, color on color) becomes illegible at distance. This generator applies procedural algorithms across 15 division patterns (fesses, pales, bends, chevrons, saltires, Nordic crosses, palls, cantons) and selects colors from a curated palette of 40 heraldic tinctures. Emblems are drawn mathematically using polar coordinate geometry. The output approximates real vexillographic practice rather than producing arbitrary noise.

The tool enforces standard aspect ratios: 2:3 (most common globally), 1:2 (British tradition), and 3:5 (US standard). Color contrast is validated to prevent adjacent fields of similar luminance. Note: this tool generates abstract designs. It does not replicate or reference any sovereign nation's flag.

Formulas

Star vertices on an emblem are computed using polar-to-Cartesian conversion. For a n-pointed star centered at (cx, cy) with outer radius R and inner radius r:

x_k = cx + R ⋅ cos(2πk2n − π2)

Where even indices k use outer radius R and odd indices use inner radius r ≈ 0.382R (the golden ratio reciprocal). Color luminance contrast between adjacent fields is checked via relative luminance:

L = 0.2126R + 0.7152G + 0.0722B

Where R, G, B are linearized sRGB channel values in range [0, 1]. Adjacent fields must differ by ≥ 0.25 in luminance to ensure legibility at distance.

Reference Data

Division Pattern	Description	Historical Example
Horizontal Bicolor	Two equal horizontal bands	Monaco, Poland, Ukraine
Horizontal Triband	Three equal horizontal stripes	Germany, Netherlands, Luxembourg
Vertical Bicolor	Two equal vertical bands	Vatican City, Algeria
Vertical Triband	Three equal vertical stripes	France, Italy, Ireland
Nordic Cross	Off-center cross shifted to hoist	Sweden, Denmark, Norway
Saltire (X-Cross)	Diagonal cross corner to corner	Scotland, Jamaica, Burundi
Chevron	Triangle from hoist side	Czech Republic, Philippines
Bend (Diagonal)	Diagonal stripe from corner	DR Congo, Tanzania
Canton	Small rectangle in upper-hoist corner	USA, Australia, Tonga
Pall (Y-shape)	Y-shaped division from corners to center	South Africa, Vanuatu
Quartered	Four equal rectangular quadrants	Panama, Dominican Republic
Horizontal Four-Stripe	Four equal horizontal bands	Mauritius, Central African Republic
Serration / Zigzag	Wavy or serrated division line	Bahrain, Qatar
Border / Fimbriation	Thin border separating fields	South Africa, Kenya
Greek Cross	Centered upright cross	Switzerland, Georgia, Tonga

Frequently Asked Questions

Each pair of adjacent color fields is checked for relative luminance contrast. The linearized sRGB luminance formula (L = 0.2126R + 0.7152G + 0.0722B) is applied, and any pair with a difference below 0.25 triggers a re-roll of one color. This mirrors the heraldic rule of tincture, which forbids placing color on color or metal on metal.

Three standard ratios are supported: 2:3 (used by ~75% of sovereign flags), 1:2 (British Commonwealth tradition), and 3:5 (United States standard). The ratio affects both the canvas dimensions and the proportional placement of divisions and emblems. Canton size, for instance, scales to occupy approximately 25% of the flag area regardless of ratio.

Yes. Stars use polar coordinate vertex computation with alternating outer/inner radii. The inner radius defaults to R × 0.382 (derived from 1/φ, the golden ratio reciprocal), producing the classic five-pointed star shape. Crescents are drawn as the difference of two overlapping circles offset by approximately 0.3R. Sunbursts use evenly-spaced triangular rays computed via angular subdivision.

Statistically unlikely but not impossible. With 15 division types, 40+ colors, and multiple emblem options, the combinatorial space exceeds 500,000 unique configurations. However, simple patterns (e.g., horizontal triband in common colors) could coincidentally resemble existing flags. The tool makes no sovereignty claims and is intended for creative and educational use.

Emblem placement follows a weighted probability: approximately 40% of generated flags include an emblem. This reflects real-world vexillographic distribution - many national flags are purely geometric. The "good flag design" principles from the North American Vexillological Association recommend simplicity, so the generator biases toward cleaner designs.

The Nordic Cross (Scandinavian Cross) shifts the vertical bar of the cross toward the hoist (left) side, typically positioned at one-third of the flag width rather than the center. This asymmetry is distinctive to Nordic countries. The generator places the vertical bar at 35% from the hoist and applies optional fimbriation (thin contrasting border) around the cross arms.