I am creating an intelligent humanoid species for DnD. I want them to have skin that has multiple colors. The colors would form patterns on the skin that would be random in each individual or could be inherited as a combination of their parents' skin patterns. There is precedent for something like this in humans, called Vitiligo (Example provided below). However, this is a condition where the skin loses melanin and gains a lighter tone in random patches. I want my species to have multiple colors rather than tones, and for it to be present in all individuals. Is it possible? Preferably without genetic engineering, as this is in a fantasy setting.
Multiple colours? Yes.
Obviously the capacity for colouration and pattern are inherited from the parent, so it stands to reason offspring will develop a variation of either or both parent's pigmentation pattern: Some features of a giraffe's spot pattern are passed on from mother to baby, according to a new study led by researchers from Penn State. And in whales: While the researchers found no clear geographical pattern to the whales' markings and vocalizations, they did find a genetic pattern: The whales' mitochondrial DNA (mtDNA), which is inherited only from the mother, indicated that groups with similar calls and markings were related.
However it really depends on the species; Dutch boxers, for example, show little consistency in marking between generations or among siblings.
Use same effect that makes human eyes and butterflies colorful. Butterflies are not colored because of pigment but because of nanoscale structures that diffract light only of specific band. Structural, not chemical variations in these sufraces drastically alter color, without need of synthesizing different chemical for each color. Each patch has slightly differently shaped particles, you end up with humans with colorful, glittering patches.
Your species has fair skin at baseline. They bleed into their skin and that is what gives its color. Just as bruises in a fair skinned individual will start purplish black or red and go to green to yellow to gold, the blood under the skin of your individuals will confer color to the overlying skin.
The breakdown system for your people is such that breakdown of blood stalls out to leave the blood at a given stage and resulting color for long periods of time. The exact color for a given place depends on the balance of enzyme expressed at the location and the enzymes / expression patterns are heritable. Blood in the skin is periodically renewed, keeping colors fresh. But the edges of a given patch will shift with time.
There are primate species with strong skin colouration, so it would only be a small stretch to extend this to humanoids. Dominant male mandrills have bright red and blue on the faces and rumps. The yellow beard appears to be hair, but yellowish skin colours are present in other monkey species.