The batman symbol is actually piecewise continuous, which can be shaped by a series of partial lines/parabolas/hyperbolas. Then of course you can use the f(|x|) concept to do reflection about the y-axis to generate the other symmetrical half. You define each equation specifically over a certain set of x values and join up the contours. Something much simpler would be this:

http://www.whitegroupmaths.com/2010/03/functions.html
But the painful part lies within finding the correct functions (which includes determining what coefficient values to choose for the various equations) to produce a decent looking Bat symbol. For this, you need someone who has too much time on his/her hands to do the tedious exploration.

Hope this helps. Peace.