Fate and Free Will in Death Note
    The cosmology of Death Note (about which we still know far too little) is largely deterministic. I base this assertion on one fact: the shinigami eyes show a person's lifespan and this lifespan shows how long a person will live unless killed by the Death Note. All other causes of death are accounted for in this number, thus lifespan is not merely "natural lifespan" or how long a person will live without meeting an accident (say being run over by the proverbial bus) or violence, but just straight out, how long they will live. This means that the cause of their death is already predetermined and thus if someone is going to murder them, they are already fated to do so and apparently there is no room for free will for that person to decide not to murder. Yes, this only truly demonstrates fate in matters of life and death, but it certainly has broader implications.

    An example: Soichiro Yagami's death. His cause of death was a gunshot. He had made the trade for the eyes, which had cut his lifespan in half. Now, had he simply died of natural causes, this wouldn't imply much. But since he died due to the actions of someone else, one has to wonder what difference the trade made. Had he not made it, would he not have been shot? Would the shot have missed or never been made at all? Or would he simply not have died of it or lived longer afterwards? If the shot would not have occurred at all (which is certainly possible) then his choice to trade for the eyes determined the actions of someone else and not merely in limiting their choices. Somehow, that trade chose his killer and cause of death.

    The only form of free will that seems to exist in this universe is connected to the Death Note itself. The Death Note lets a user kill with no regard for lifespan as well as allowing them to choose method (interestingly, while one cannot make the person slated to die in the Death Note kill anyone else, the method chosen for their death could make someone else a murderer). One could argue that it is the shinigami that are the instrument of free will rather than the Death Note, due to the fact that they can change fates through making the trade for the eyes, but this can only be done with a Death Note owner, thus linking this ability back to the DN itself. Also, the shinigami themselves have lifespans, suggesting they are just as subject to fate as humans (and like humans, the only things that affect their lifespans have to do with the Death Note). And a shinigami must have a Death Note, perhaps because otherwise they have no free will and no ability to act outside of predetermined actions.

   So if the Death Note is the only instrument of free will in this cosmology, one must wonder what it is, exactly, and where it comes from. The shinigami king gives the DN to the others, but we don't know where he gets them from. I don't know what the source is, but given all the above, I really wish I did!

Magickal and Mythological Correspondences and Characters

Elements
    So, we'll start with perhaps the simplest correspondences: elemental. In this case, I am applying the four Western elements to the four main characters of Death Note, whom I am defining as Light, the protagonist, and his main antagonists. One could of course quarrel with this assessment of the main characters but it seems fairly accurate to me due to their roles in the story.
Air: Near. This one's easy. Near is all about intellect and almost nothing else.
Fire: Light. Fire represents will as well as charisma and both are defining characteristics of Light. Also, a fire sign's main weakness is a tendency towards arrogance. And then there is the name...
Water: Mello. In fanfic, Mello tends to be associated with fire and there are definite reasons for it. It works very well on a metaphorical level. In classical elemental terms, though, he is a water character because he is nearly completely defined and driven by emotion. (Admittedly, were I making an astrological chart for how he seems to me, he would most likely be a fire sign rising with a water sign sun and moon - probably Scorpio Sun, Cancer moon, and Aries rising.)
Earth: L. This one is the most difficult to explain, but I still think it works. L is earth in the way he sees patterns and in his practicality. Yes, he seems whimsical, but everything he does has a purpose.

Aspects of Fate
     In this case, I mean the Greek aspects of Fate: Clotho, Lachesis, and Atropos. For these, I am using LMN because they do all three work towards the same goal. I am specifically excluding Light or Kira from this even though on the surface he might appear to be a good Atropos because the role of Atropos is to cut the threads when it is their time and their role in the tapestry is done. Kira cuts them early and damages the weave (note this goes along with my earlier discussion of the Death Note as an instrument of free will, outside of fate).

     I can see this done two different ways and a case can be made for either, depending on whether personality or role in the manga is most important. I will, of course, show you both.

The first one I thought of and I guess therefore the most instinctively obvious to me is this one:
Clotho: Mello. He makes something useful out of Chaos and he is definitely the one most in tune with Chaos in general.
Lachesis: L. He weaves the disparate threads together and sees the shape of the whole tapestry.
Atropos:: Near. He takes the work of the others and brings things to a close, cutting the threads when their time is done

Second version:
Clotho: L. He starts the work, sees the pattern when no one else can and thus imposes Order on Chaos, making it useful and comprehensible.
Lachesis: Near. He takes the threads spun by L and weaves them together into the tapestry, seeing and revealing the pattern
Atropos: Mello. The only one of the three who killed and thus the one who cuts the threads, makes the sacrifices necessary for the good of the tapestry as a whole. And yes, that has chapter 99 implications, too.