What is it that undulates in a particle? When there is a wave, something is undulating. In the example of a rope, the rope is what undulates. In the case of a ripple on a pond, the water is undulating, and when a sound wave propagates, the air is undulating. The question is: in the case of a particle, what undulates?
 A: The undulations are of the probability amplitude for the particle to be someplace. The notion of probability amplitude is fundamental, and cannot be reduced to anything more primitive. It is described on Wikipedia under "superposition principle". The undulations are in the space of all possible universes, so that two particles are described by undulations in the 6 dimensional space of all possible pairs of positions, three particles are described by undulations in 9 dimensions. There is no physical way of making it like waves on water or sound in air, because physical waves travel in three dimensions of space. 
If you are asking about classical fields, like E and B fields, there are not undulations in anything either. They are the primitive things out of which things like atoms and water are built. You can make classical fields out of particles if they have the right statistics, and these fields, when they are made of matter, are called Bose-Einstein condensates or superfluids, depending on the density.
