The Formula Behind the Art
Golden Angle Formula
137.508°
The same number sunflowers use to pack seeds. The same angle pinecones spiral by. STILL Studio applies it to names — turning letters into numbers, numbers into a hue, and that hue into a one-of-a-kind painting.
What is the golden angle formula?
The golden angle is approximately 137.508 degrees (written precisely as 137°30′28″). It comes from the golden ratio φ ≈ 1.618:
Nature uses it because it is irrational — its decimal expansion never repeats, so consecutive seeds or petals placed at that angular offset never land in the same spot. A sunflower with 34 clockwise spirals and 55 counter-clockwise spirals is the golden angle at work: every seed is packed as tightly as possible without any gaps.
The same property makes it useful for color: rotate a hue by 137.508° and you always land somewhere new on the wheel. Apply it 26 times (once per letter of the alphabet) and you get 26 colors that are spread as evenly as possible — no two are the same, none cluster together.
How does 137.508° turn a name into a color?
The formula is three steps:
- 1
Assign a value to each letter
A=1, B=2, C=3… Z=26. No arbitrary mapping — just the alphabet's natural order.
- 2
Sum the letters in the name
Every letter in the name contributes its value. The sum is unique to the spelling of that name.
- 3
Multiply by 137.508, read the color wheel
Multiply the sum by 137.508. Take the remainder when divided by 360. That is the hue angle — a precise point on the color wheel.
Worked example: "EMMA"
sum: 5 + 13 + 13 + 1 = 32
hue: 32 × 137.508 = 4400.256 → 4400.256 mod 360 = 80.3°
EMMA lands at 80.3° on the color wheel — a warm yellow-green. A different spelling gives a different hue.
Why the golden angle produces good colors
Most color palette generators pick colors by eye or use fixed formulas — complementary, triadic, analogous. Those methods work, but they repeat. The golden angle never repeats.
Because 137.508 is irrational, the sequence of hues it generates is maximally spread: each new color lands as far as possible from every color that came before it. This is exactly the property that makes sunflower seeds pack without gaps — and it is what makes family name palettes look balanced without any designer input.
A four-person family gets four colors. A seven-person family gets seven colors. In every case they spread across the wheel naturally, no two clashing, none drowning the others out.
See your family's golden angle palette
Enter your family's names and watch the formula run in real time. Each letter shows its value. Each name shows its hue. Then choose a master artist — Van Gogh, Monet, Hokusai and more — and AI paints your palette in their style.
Try the formula — freeNo signup. See your colors instantly. From $9.99 to download.
Frequently asked questions
Is 137.508 the exact value?
The precise value is 180° × (3 − √5) ≈ 137.50776...°. It is irrational — it goes on forever without repeating. 137.508 is a commonly used approximation. STILL Studio uses the full precision value internally.
Why does it appear in sunflowers and pinecones?
Plants grow new seeds or scales from a central point, one at a time. If each new element rotates by a rational fraction of a circle, they eventually line up and leave gaps. The golden angle is the rotation that wastes the least space — an outcome natural selection arrived at independently, in many unrelated plant families.
Can two names ever produce the same color?
Two names that sum to the same number get the same hue. For example, 'Ana' (1+14+1=16) and 'Dan' (4+1+14=19) are different, but a longer name could coincidentally share a sum. In practice this is rare within a family, and the saturation and lightness are also adjusted per person, so even matching hues look distinct in the final painting.
Where can I read more about the golden angle in math?
STILL Studio has a long-form explainer at /blog/the-golden-angle covering the mathematics, the Fibonacci connection, and the history of how plants were discovered to use it.
Want the deep dive?
The blog covers sunflowers, Fibonacci, and the full math history.