D U N
Dun is the gene TBX3 on Chromosome 8. There are three allele mutations on the locus. The dominant dun allele, D, dilutes the coat and gives primitive markings. A dun horse will always have a dorsal stripe that runs the entire length of the spine (including through the tail). Other primitive markings may appear to varying degrees including ear tips and bars, face masks and cobwebbing, shoulder stripes, barbs off the dorsal stripe, leg barring, and guard hairs or frosting in the mane and tail.
The dominant dun allele on a bay base is a bay dun, also simply called dun. This is the original color of primitive horses. Black duns are commonly called grulla (Spanish for "crane," NOT grullo; they are not masculine/feminine forms, they are not even the same language - grullo is Italian and it is a rude slang term for "foolish" or "idiot"). Red-based horses with a dominant dun allele are red duns.
E_ A_ D_ or E_ aa D_ or ee D_
N O T - D U N
The more recently discovered mutation of the dun gene is called nd1, or not-dun 1. It is recessive to the dominant dun allele and dominant to the not-dun 2 (previously known as d) allele. The not-dun 1 mutation adds various primitive markings without diluting the body, though slight dilution may occur when it is homozygous. This is not a dun horse, but a horse with primitive factors. Not-dun 2 does nothing to the base coat; no dilution and no primitives.
E_ A_ nd1_ or E_ aa nd1_ or ee nd1_
E_ A_ nd2nd2 or E_ aa nd2nd2 or ee nd2nd2
E_ A_ nd2nd2 or E_ aa nd2nd2 or ee nd2nd2