Zebra striping

What it does

Crossing two of them

Its gene carrot

Gene key

horsegenetics.natural_zebra

Priority

68 — after every gene that decides the base colour, before the white-spotting loci

Alleles

Zeb n

Outcomes

wild, shadow-striped, zebra-striped

Inheritance

codominant — one copy is visible, two are louder

Default allele

n

Wild frequency

1 in 60 per allele — so about 3% of wild horses are shadow-striped and 0.03% fully striped

Founder draws

1 × nextFloat()

Deterministic

no when expressed

Epigenetic draws

1 long + 4 nextFloat

Field

coat.pattern.ZebraStripes

Codominant, and the carrier is not invisible

One copy suppresses melanin part of the way rather than all of it, which is what a plains zebra’s shadow stripes look like: faint brownish bands between the strong ones, on some southern populations. So the locus has three phenotypes you can tell apart on sight, and a player can see that a horse is worth breeding before they have the pair. Both outcomes run the same painter and draw the same five epigenetic knobs, differing only in the strength — so a shadow-striped mare and her fully striped foal wear the same pattern at two intensities, and the two expressions cannot drift apart.

The stripe map, region by region

A zebra’s stripes are not one field of parallel bars. They are a developmental map expressed over a three-dimensional body: the same patterning machinery lands differently on differently-shaped anatomy, so the direction changes with the region. A dark dorsal stripe along the spine acts as the central organiser, and most torso stripes descend from it, changing direction, width and density as they pass over curved anatomy.

The rump is one lerp, and no special case

The hardest thing on that list is the hindquarters, because a field of parallel planes structurally cannot produce an arc. It turns out not to need a second field:

double radial = Math.sqrt(dx * dx + dy * dy);          // distance from a point on the hip
double toArcs = 1.0 - smooth01(fx / RUMP_END);         // 1 at the rump, 0 by the flank
double along  = point.x() + (radial - point.x()) * toArcs;

A vertical band is a plane of constant x. An arc round the hip is a circle of constant radius from a point on it. Both are a phase, so the two are simply lerped — and every intermediate value between them is one of the angled, curving bands a real zebra wears over the flank, which is the part that a field built out of planes and a field built out of circles both get wrong on their own.

The five epigenetic knobs

Drawn off the expressing copy, in this order. A foal that inherits the copy inherits the pattern exactly.

Those last two are where the real species differences live. A plains zebra has moderately broad bands, often reduced on the lower leg and belly. Grévy’s has the narrowest, densest striping of the living zebras, continued to the hooves. A mountain zebra sits between, with cleaner high-contrast bands. Rather than model three species, the gene draws from a range that spans them, so two striped horses can look like different animals.

The chevron is load-bearing

The phase carries a small slant on |z|, bending each band into a shallow chevron over the back. This is the same trick BodyStripes uses and for the same reason: without it, every face perpendicular to X — the chest, the rump, the front and back of every leg — sits at one phase and renders as a flat band of solid stripe or solid coat. It is symmetric left to right, so the horse does not look lopsided.

Symmetry is the right answer here and the wrong one for brindle, which is why the two genes do not share a field. A zebra’s two sides broadly match; a brindle horse’s deliberately do not.

Which way round a zebra is

Ask which of a zebra’s two colours is the animal and which is the marking, and the biology answers plainly. Hair follicles carry melanocytes; in the dark bands they deposit melanin into the growing hair, and in the white ones signalling suppresses that. The white stripe is not a white pigment — it is an absence of the dark one, and the dark state is the default. A zebra is a dark animal with the colour taken out in bands.

That is exactly the shape of phase 1, which may only ever take pigment away, and it is why this gene can be natural at all. It whitens the gaps through PigmentField.whiten and never touches the bands. The horse underneath — whatever extension, agouti, the dilutions and grey have made of it by priority 68 — is the striping.

Not modelled

• Species. There is one locus, not a plains / mountain / Grévy’s trichotomy — the knob ranges span them instead.
• Facial stripes that curve round the eye and nostril. Below the sheet’s resolution; the head gets narrow bands and a dark muzzle.
• A reaction–diffusion simulation. Zebra striping is usually modelled as a Turing pattern — local chemical signals producing repeated spacing without any gene specifying “stripe number 17 here”. What that buys visually at this resolution is spacing and contrast, both of which are knobs here, so the coat is drawn directly rather than simulated. The consequence of the Turing account that does matter is modelled: the pattern changes shape with body geometry, which is the whole point of ZebraStripes being a body map.
• Stripes as an individual fingerprint. They are, in the sense that every horse’s stored values give it its own arrangement — but nothing in the mod identifies a horse by them.