These butterflies are quite interesting. There are two adult color phases in the females, the light phase shown here and a dark phase-the black tiger swallowtail -which is apparently involved in a mimicry system with the pipevine swallowtail. See this site for more pictures of larvae and adults.
The genetics of this color system is quite interesting. First, realize that unlike mammals, the females are "XY" , usually denoted "ZW", and the males are ZZ. So the females in butterflies are called heterogametic, since they produce gametes which can have either of the thew two different sex chromosomes. In contrast in mammals the males are the heterogametic sex, with the females being homogametic.
According to Scriber et al (1996), the genetic system related to which form the butterfly becomes (yellow or black tiger swallowtails) involves two loci. The first locus is a W linked locus, that has an allele b that when present leads to the production of the black, or melanistic, black swallowtail. Here I am following the notation given here.
Since the females are ZW, black tiger swallowtail females only produce black tiger female offspring while the yellow swallow tail females only produce yellow female offspring. The males always have yellow wings.
The second locus, which is Z linked that has an allele scan which can "suppress" the expression of the W linked allele b . So presumably a female that has the b allele on her W chromosome would be the black tiger form if she has scan at the second locus.
So to give an idea about how this works, suppose a female black swallowtail butterfly has genotype b s (where s by itself represents the non suppressor allele mates with a male who is heterozygous scan/s. All the male offspring will, of course be yellow, since the males do not have the W chromosome with its b allele. Half the female offspring will have genotype b s and hence be black. The other half will have genotype b scan and will be yellow.
On occasion, a butterfly is found with a one black swallowtail wing and one yellow swallowtail wing. For instance, to the left is a picture taken by Jay Joslin on a cell phone camera. These appear to be gynandromorphs, animals which are mosaics with a mixture of male and female characteristics. The term is not used for humans. In insects, gynandromorphs typically are genetic mosaics, some cells being "XX", other cells being "XY". Here is a good discussion of gynandromorphs showing different types of gynandromorphs in tiger swallowtails.
Funny that this concept arises now, since I am currently reading Middlesex by Jeffrey Eugenides. The protagonist in this book is a chromosomal male who is pseudohermaphrodite, with ambiguous genitalia. But this is due to a recessive allele on chromosome 5 of a gene for a an enzyme called 5-Alpha Reductase. This enzyme catalyzes the conversion of testosterone to another sterol called DHT. This is the molecule associated with certain types of baldness but more importantly DHT is required for normal development of the external male genitalia. Here is a good discussion of the genetics of 5-Alpha Reductase deficiency. So Cal, Eugenides' protagonist is not a genetic mosaic as are the gynandromorphs in the insect world. There is more to the genetics of Middlesex...but that will have to wait.
But situations analogous to insect gynandromorphs, in that individuals are genetic mosaics with respect to the sex chromosomes, do happen in people. For instance, persons with Klinefelter's syndrome, are sometimes mosaics. This happens when the sex chromosomes fail to segregate early in development leading to some lines of cells in the embryo that are XXY and others which are XY. See this reference. We do not find the sort of symmetric situations found in butterflies-male external characteristics on one side and female on the other- in mammals because mammalian development is indeterminate as opposed to determinate meaning that the fate of cells in insects is set very early on. So which cells end up on the left vs right side of the insect is set at the first division of the zygote.
Also sex germination in butterflies is not exactly the same as in people since what is critical is the number of Z chromosomes relative to the number of W chromosomes. So Butterflies that are ZW are female but butterflies with a W chromosome but more than one Z chromosome may be male depending on the species. So if a non disjunction event happens in the first division leading to the 2 cell embryo in a black swallowtail female , one side of the insect will end up having ZW cells and be the black swallowtail phenotype. The other side will presumably end up ZZW, which in butterflies is (at least often) male. This side will have the yellow tiger swallowtail coloration.
J. Mark Scriber, Robert H. Hagen, Robert C. Lederhouse Evolution, Vol. 50, No. 1 (Feb., 1996), pp. 222-236
Reed, Robert D. and Sperling, Felix A. H. 2002. Papilionidae. The Swallowtail Butterflies. Version 21 February 2002 (complete). http://tolweb.org/Papilionidae/12177/2002.02.21 in The Tree of Life Web Project, http://tolweb.org/