Usually those crunchy, dirty basses used in Electro or Dubstep are made using FM Synthesis (Frequency Modulation). It also might be Additive Synthesis of some saw waves with a lot of effects, but FM is more common for those type of things. It's important that you use saw waves for those basses, as they have the richest harmonic content and can allow you to do very deep effects.
In audio and music, frequency modulation synthesis (or FM synthesis) is a form of audio synthesis where the timbre of a simple waveform (such as a square, triangle, or sawtooth) is changed by modulating its frequency with a modulator frequency that is also in the audio range, resulting in a more complex waveform and a different-sounding tone that can also be described as "gritty" if it is a thick and dark timbre.
So basically, it's the exact same thing as LFO-ing the pitch, except instead of a Low-Frequency Waveform (LFO), you use a normal pitch sound, resulting in a higher frequency, resulting in an extremely fast modulation, which makes a really special sound. I do believe Logic has an FM synthesizer, but if it doesn't or if it's not really good, I really recommend FM8 by Native Instruments.
So it's kind of like the layering you said, except for waveforms. There may be several harmonic waveforms (like square/triangle/saw) stacked together in the synthesizer, maybe affecting each other in one way or another. There is probably also a bass sine (something that is extremely popular with basses, especially in dance/electro/club-ish music) which is basically just a simple sine wave set to a few octaves lower than the rest of the synth, which really fills up the low frequencies and fattens up your bass a TON. That simple, though that awesome.
I also noticed that there are little treble-hits, that sound like no more than a simple sine wave synth, or maybe a richer waveform (square/triangle/saw (but I doubt it's a saw) with a low-pass filter (that might also be automated with an ADSR envelope with the attack going down).
Hop this helps, and I can't wait to hear what music you'll create with this knowledge!