I kinda like the concept of mathematical magic. Use the laws of nature and reality to your advantage with the power of math. It frees you of the restraint of requiring faith and following a religion of any sort (kinda makes me sound like a heretic), and a good knowledge of math (the more advanced, the better) can make you do all kinds of things. Lastly, another branch can be applied to this method of magic, fractals. Fractal magic, and being able to draw other forms of magic by chaining them together via fractal designs.
In hindsight, this makes Vector probably the deadliest mage amongst us, provided she uses this branch of magic/math to it's fullest potential. She definitely has the mind to really mess people up with it.
I would imagine magic runes, crests, sigils, and etc. would look pretty, badass, and awesome while being quite functional and efficiently drawn (vector-based drawing, rather than chalks and raster designs, which can render them as large or small as you want them without compromise to quality), and the executions would be beautiful and consistent overall.
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I think the most appealing aspects of Mathemagicks would be the fact that you ouldn't need to sacrifice or draw blood to gain control or anything of the sort (or gain permissions), no unneccessary chanting (unless you have mnemonics for the equations), no sacrifice of your first-born or surrendering yourself to a greater being. Essentially, you just need to be really really smart. Your most powerful weapons are a calculator, paper, and a pencil, and maybe a handheld computer. Unless you can do all the work in your head.
Now I'm thinking of the Calculator/Arithmatician job class from Final Fantasy Tactics. Deadliest combat unit in that game.
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Oh yeah, and I also forgot to mention; since it's non-elemental based (light/dark), nor spiritually-based; even the most powrful/skilled mathemagicians cannot be detected by even the most sensitive and most powerful sorcerers/priests/zealots. I call that one hell of an advantage.
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A pretty nasty spell example I came up with is essentially nicknamed the Danmaku (Bullet-Hell), after the arcade-style SHMUPs. It's a fractal-based mathemagic attack. You have your initial casting rune drawn out (slowly and then rapidly cools the air, thus making ice rounds out of the immediate vicinity), following up with a kinetic punch (essentially firing them like bullets). The initial rune (must be large) sets the stage for fractalling, and buds smaller versions of the same spell as it branches within itself (from center-outward branches inside the runes). Cast from the smallest runes up to the largest initial rune, and you can easily go from the tiny 4.4mm round of ice bullets, to something comparable to a howitzer cannon round as the final shot. Perforate your targets before you punch them incredibly hard. They'd be lucky if there's anything left of them after the casting is over.
Ice is one example. You can also fire glass, molten, and compressed air (shockwave) rounds. Oh yeah, and "bullet" velocity is your choice. You can even just make it a series of shockwave rounds with no forward/backward movement, and just make it a repeat-pressure-explosive space. Sorta like the anomalies in STALKER.
Fractal-magic can also yield some pretty kickass fireworks and ice sculpture displays.
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Great, now I have a pretty badass rune/series idea that essentially makes a magic revolver, as well as using the bullet cartridge in the revolver a rune-container which can inter-change magic spells. Just pull the activation rune, and the rest acts together in unison, activating the magic-class round, and pushing it into the accelerator runes, thus making literally a magic gun loaded with magic bullets. I gotta put some time aside to draw it. It looks too awesome in my mind not to.