The Experimental Seven: Colours Computed, Not Chosen

When we published the four colour sets of the Bundu Order — minerals, heritage tones, system colours, and the experimental set — readers asked a fair question: you named the colours, but where are they? This post answers it for the newest set, and it answers something deeper: where these seven colours come from. The answer is: nowhere. No moodboard, no designer's eye, no reference photo. Every value below is the output of a computation whose only inputs are prime numbers and the Bundu Order. We chose nothing but the names.

Why seven — and why the heptagon

Seven is the covenant number of the Order, and every colour set is sealed at seven — four sets of seven making 28, the seventh triangular number and a perfect number. But for the experimental set, seven earns its place a second time, through geometry.

Seven equally spaced directions around the colour wheel form a regular heptagon — and the regular heptagon holds a famous distinction: it is the first regular polygon that provably cannot be constructed with compass and straightedge. A triangle can be drawn by hand. A square, a pentagon, a hexagon — all constructible. The heptagon cannot be drawn by classical means at all. It can only be computed.

That is the whole philosophy of this colour set in one shape. These colours cannot be picked by hand. They can only be solved.

The derivation — every input is a prime or an Order number

Hue. The seven hues sit at the vertices of the heptagon: spacing of 360°/7 ≈ 51.43°, rotated by 17° — the founding prime of the Order, the 7th prime. So:

hue(k) = 17 + k × (360/7), for k = 0 to 6.

Saturation. One value for all seven: 61 — prime. Tinted containers use saturations 23 (dark) and 29 (light) — twin primes.

Surfaces. The backgrounds these colours live on are themselves prime-computed: dark surfaces stand at lightness 2, 3, 5, 7, 11, 13, 17 above black; light surfaces at 100 minus each prime. Tinted containers sit at the L17 step (dark) and L100−11 step (light).

Lightness — solved, never picked. For every colour, the lightness of each foreground is found by binary search until it clears its prime contrast floor: at least 7:1 (P7 — stricter than WCAG AAA's threshold is strict) for all text, at least 3:1 (P3) for interface accents. The luminance formula is the standard WCAG calculation; the primes decide every threshold, every surface step, every saturation, and every hue. The search runs until the measured ratio lands just above the prime — which is why every value below reads 7.05, 7.08, 7.13: the mathematics parked each colour as close to its prime floor as the hex grid allows.

What remains for a human to choose? Only the names — working labels drawn from the African landscape at each hue.

The seven, shown

(Each swatch pair shows the dark-theme value, then the light-theme value. If the swatches don't render in your reader, the hex codes are the truth anyway — they always were.)

1. ember — k = 0, hue = 17.00°

#DA8766 (7.06:1 on dark base) · #843D20 (7.08:1 on light base) Containers: #352721 / #EBDFDB · on-container #EBA68A / #7A3115 (both ≥7:1) The warm anchor of the heptagon — the vertex the founding prime itself points to, since its hue is 17. Candidate jobs: warm accents, chart series 1.

2. acacia — k = 1, hue = 68.43°

#93A528 (7.08:1) · #4D5615 (7.11:1) Containers: #333521 / #E9EBDB · on-container #B6CE23 / #48510E The yellow-green the mineral set deliberately avoids — which is exactly why the heptagon lands here. Candidate jobs: organic accents, chart series 2.

3. fern — k = 2, hue = 119.86°

#2CB42B (7.09:1) · #175E17 (7.13:1) Containers: #213521 / #DBEBDB · on-container #28DB28 / #0F570F Pure green — a hue malachite (a deep blue-green) never occupies. Candidate jobs: growth accents, chart series 3.

4. lagoon — k = 3, hue = 171.29°

#2AAE9B (7.05:1) · #165B51 (7.13:1) Containers: #213532 / #DBEBE9 · on-container #24D6BC / #0E554B The teal vertex. Candidate jobs: water and clarity accents, chart series 4.

5. storm — k = 4, hue = 222.71°

#7E9BE0 (7.08:1) · #284CA6 (7.07:1) Containers: #212735 / #DBE0EB · on-container #99B2EE / #1A409B A rain-sky blue between cobalt and sodalite without touching either. Candidate jobs: cool accents, chart series 5.

6. dusk — k = 5, hue = 274.14°

#BA87E2 (7.07:1) · #742AAD (7.06:1) Containers: #2D2135 / #E4DBEB · on-container #CC9FEF / #661B9E The violet vertex — brighter and bluer than tanzanite's territory. Candidate jobs: twilight accents, chart series 6.

7. protea — k = 6, hue = 325.57°

#DF7BB4 (7.05:1) · #932464 (7.06:1) Containers: #35212D / #EBDBE4 · on-container #ED98C9 / #841656 Named for the king protea, the continent's boldest bloom — the magenta the mineral palette has never had. Candidate jobs: bloom accents, chart series 7.

How to use them

The experimental seven exist for jobs the other three sets do not own. The minerals carry brand identity; the heritage tones carry atmosphere; the system colours carry state. What none of them provides is a set of maximally separated, equally weighted hues — and that is precisely what a heptagon on the colour wheel is. Seven categories in a chart, seven segments in a breakdown, seven equal voices in a visualisation: this is the palette. Beyond data, they are the proving ground for accents — illustration, seasonal moments, candidate identities. A colour is promoted out of the experimental set only when it earns a permanent job no other set owns and passes the registry audit. Until then, every one of them is exactly what its derivation says: an experiment — conducted, measured, and shown.

The honest footnote

The luminance mathematics underneath the contrast ratios is the standard WCAG formula — we do not rewrite physics. What the primes and the Order decide is everything a designer would otherwise decide: the number of colours (7), the hue positions (heptagon, offset by the founding prime 17), the saturations (61; containers 23 and 29), the surfaces they stand on (the prime ladder 2·3·5·7·11·13·17), and the floors every foreground must clear (P3, P7). An earlier draft of this set used hand-picked hues with prime floors; those values are superseded — a colour set that claims to be computed must be computed all the way down. This one is.

Ndiri nekuti tiri — solved together, legible for everyone.