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A technique in superhero comics is to revise myths, recasting them with superheroes. In contrast to mythic heroes, comic book superheroes have limited roles to maintain the status quo by defeating super villains, typically. Nonetheless, the life stories of superheroes often match those of mythic heroes, even so far as having origins as ancient gods. Wonder Woman is a truly classical example of this, since she comes from a race of immortal Amazons.
In the graphic novel written by Greg Rucka and illustrated by J.G. Jones and W. von Grawbadger (2002: 34–35), The Hiketeia, she encounters other elements from classical mythology.



Wonder Woman: The Hiketeia, text by Greg Rucka; art by J.G. Jones (penciller) , W. von Grawbadger (inker), D. Stewart (colorist), and T. Klein (letterer), (2002) (New York: DC Comics, 34–35)
In this example, the Furies, called by their Greek name of Erinyes, have lately come to Earth and are confronted by Wonder Woman for the first time. They are here to punish Wonder Woman, who is protecting Danielle, a young vigilante. Danielle does not have a lucky ending. She ends in suicide, which satisfies the Furies and saves Wonder Woman and Batman from their wrath. This story is an example of revisionist myth since the Furies are taking on their archetypal roles as nemeses in a modern setting. Nemesis is an important part of the basic myth of the hero. This can be shown using the following structural notation system.
Mythic algebra can be used to model stories and show patterns. As a formal system, it may identify tropes for either the writer or reader, and the artist or viewer. While the choices of these tropes occur in a social context, aside from that they still may have a structure. Such formalism does not require determinism, but rather presents the most logical possibilities granted by the language. It consists of six set elements (p,q,x,y,s,t) representing people and their acts, things and their actions, space, and time. For a person (p)’s acts I have been using q, and for things x and their actions y, space s and time t.. Mappings of these elements occur between sets with either mythic M or real R status. The algebra’s contents can be briefly listed as: (p,q,x,y,s,t), M, R, M/R, R/M, →, +, –
Here the slash / stands for a mapping of a set element from one set to another, and the “state” of the set is indicated by mythic M or real R, so that M/R means an element has moved from a mythic set into a real set, and R/M means an element has moved from a real set into a mythic set. There are three basic operations +, – , → of addition, subtraction, or the transform → can just alter elements or states by switching them.
An example of the transform use can occur with other kinds of sets, say if we define status not by mythic or real but by heroic, H, or villainous, V. Then H→V would mean that a hero set has become a villain set. In an attempt to avoid redundancy and achieve economy of notation, these set states can stand for any elements they may contain. To show a normal person becoming a hero, we can write (p)→H. To show a villain becoming a regular person, we can write V→(p). We now have all of the notational tools that we need.
Whether their stories convey social or personal adventures, heroes can be fit into a life cycle model, such as Joseph Campbell’s interpretation combined with a mirror-image tragic hero pattern. Campbell has a three-stage analysis of the hero: separation from the world, initiation into heroic status, and return to society with a benefit to save it (1968: 30). One may call this a positive, upswinging pattern with no apparent downside. In print, Campbell ignores any downward swing, as if it isn’t part of the hero’s story. Glossing over it in his book The Hero With a Thousand Faces, he notes “But a deterioration may take place in the character of the representative of the father… The upholding idea of the community is lost. Force is all that binds it. The emperor becomes the tyrant ogre (Herod-Nimrod), the usurper from whom the world is now to be saved” (1968: 349). 
I suggest that these three stages are only one half of the hero’s story instead of the complete one. There is a second half of the story, the downside. The tragic downswing may be interpreted as the declining years of a hero who may even become a villain, wherein hubris is punished by nemesis, or a character flaw hamartia leads to collapse.
Hamartia is the fatal character flaw that manifests once the hero has done his job and saved society. Aristotle remarks on it in Chap. XIII of Poetics when discussing plot, “The change of fortune should be not from bad to good, but, reversely, from good to bad. It should come about as the result not of vice, but of some great error or frailty, in a character either such as we have described, or better rather than worse” (1961: 76). It leads to hubris, a conceited pride, perhaps that he should lord it over society or flaunt the rule of the gods. This results in his opponent, nemesis, arising to cut him down to size. Herbert Ross (1968: 208) commented about nemesis:
The second divine entity of this name is an abstraction – i.e , indignant disapproval of wrongdoing, particularly the disapproval of the gods, with the consequent punishment of a sinful or overly prosperous man; and the eventual personification of that disapproval (first traceable in Hesiod).
If the fallen hero is lucky, he survives as a mere commoner, back where he began long ago. For a more tragic hero, the hamartia may consist in letting himself transform into a villain. Darth Vader is an example of one. Such transformations represent the peak of a career, whether the subsequent decline is into villainy or just the playing out of hamartia and hubris.
Whether it ends in self sacrifice or just with a defeated villain, the structure of the story remains the same. We have a pattern like a life cycle, with a beginning of positive growth and then a decline to a final end. As a sequential narrative, the algebra of each stage would line up as: (p), (p)R/M, (p)→H, (p)M/R, H→V, (p)M/R, H→(p),V→(p), (p)R/M. Arranged visually, the cycle looks like this:


There is a convenient symmetry in this, with diametrically opposite events. The first separation from society is physical, whereas the second separation is a social separation due to the attitudes of hamartia and hubris alienating the hero. The hero’s first return is to home society, and the final return is to commoner status. The first initiation is into hero status among mythic settings, while nemesis initiates the hero into personal defeat and humility, undoing his special status.
Mythic algebra shows some features of this symmetry. We can use sets to map a person p as they travel from mythic settings to real or vice versa. An abbreviated use of the algebra gives (p)R/M when the hero separates from his world R to go to the mythic one M, and (p)M/R when he returns to R. These are balanced by (p)M/R at the hubris stage and (p)R/M at the return to normalcy, although it is for a different character than the hero. In summary, the symmetric functions pair off as follows:
Separation: (p)R/M, and Return to Normal: (p)R/M
Return: (p)M/R, and Hubris: (p)M/R
As far as the algebra itself is concerned, what changes in pairs is that the M and R states switch.
As a final symmetry, we may note that the spot where hamartia and hubris occur shares a transit event with nemeses. Once hubris occurs, the gods may launch the nemeses from the mythic land M. There is a (p)M/R occurrence when mythic creatures (p) come to R, Earth, to knock the hero down to humble size. In the actual nemesis and collapse stage the creatures finally meet their target and inflict the punishment of the gods. The nemeses may take a while to find the hero and inflict his punishment. For example, the Furies were searching for Orestes, seeming two steps behind him before catching up. Thus, we have the expression, “He met his nemesis.” Once their mission is done and the collapse has occurred, the nemeses themselves can return to their mythic land from the real one. There is a reverse transit (p)R/M when the creatures return to M, their mythic realm.
In The Hiketeia, the Furies’ return to their underworld (p)R/M is implied on the last page of the story as they walk away from the Amazons’ embassy in New York City. The above image of them confronted by Wonder Woman is the first acknowledgement that they have come to Earth, (p)M/R. The layouts and framing of this image fit a subtext of the hero cycle. Wonder Woman floats in the air, looking down upon the Furies as if she were the dominant and more powerful person. Yet the Furies are the stronger ones who could destroy her. But they have come from their underworld, so it is fitting that they are looking up to her. 
This confrontation occurs across the street from the Amazons’ embassy. This embassy itself serves as a setting for Danielle to go through the hero cycle. What is an embassy but the territory of another land, in this case a mythic land of Amazons. Danielle separates from the mundane world when she enters the embassy, (p)R/M. Her purpose is to seek protection from Batman, who wants to arrest her for killing criminals. Knowledgeable about ancient Greece, Danielle comes as a supplicant under the custom of hiketeia.
The hiketeia ritual initiates Danielle to become a protegee of Wonder Woman, (p)→H. Danielle returns to the real world when she flees the embassy, (p)M/R. The myth was revised in that she remains a nonhero, while the Furies’ target is Wonder Woman instead of Danielle. Wonder Woman has the hubris to take on the ancient custom of hiketeia, and she and Batman are the ones attacked as they try to stop Danielle from committing suicide.
Batman is Danielle’s earthly nemesis, of course, and does confront her, but Wonder Woman intervenes to fight him. In the Nemesis stage, Wonder Woman is actually fighting with two kinds of nemeses: Batman and the Furies. Danielle leaps from a cliff, her death ending her protegee status, H→(p), and also ending the fight. Life returns to normal for Wonder Woman and Batman. The story ends as it began, with Wonder Woman looking out of her embassy window at the Furies.
Could the ancient Greeks have ever imagined that their Furies would meet up with Wonder Woman thousands of years later? This hero cycle does not mean that all hero stories have to follow this structure, if only because any storyteller can embellish and improvise the tale to make it different. If hero cycles are universal – whether Campbell’s, the tragic Greek, or their combination – they are only so as logical possibilities. 
Heroes and villains don’t have to change. The basic hero cycle is a kind of template, a starting point for anyone to fill in the blanks or alter the pattern. And part of the joy of humanity is the endless creativity we have to come up with new stories, even if they begin as revisions of myths.
REFERENCES
Aristotle (1961) Aristotle’s Poetics Trans. S.H. Butcher (New York: Hill and Wang) http://www.gutenberg.org/ebooks/1974. Accessed 28 July 2012
Campbell, J. (1968) The Hero With a Thousand Faces 2nd ed. (Princeton: Princeton University Press)
Griffin, M. (2001) “An Expanded, Narrative Algebra for Mythic Spacetime”. Journal of Literary Semantics, 30 (2) DOI: 10.1515/jlse.2001.004
Griffin, M. (2000) “Mythic Spacetime”. Journal of Literary Semantics, 29 (1) DOI: 10.1515/jlse.2000.29.1.61
Ross, H. J. (1968: 208) “Nemesis”, in Encyclopedia Britannica 14th ed. v 16 (Chicago: William Benton)
Rucka, G. (w),  Jones, J.G. (p) and W. von Grawbadger (i) (2002) Wonder Woman: The Hiketeia (New York: DC Comics, 34–35)